Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

So I am trying to help a friend do her homework and I am a bit stuck.

$$8x+3 = 3x^2$$

I can look at this and see that the answer is $3$, but I am having a hard time remembering how to solve for $x$ in this situation.

Could someone be so kind as to break down the steps in solving for $x$.

Thanks in advance for replies.

share|cite|improve this question
Thank you all for your comments it would seem i didnt give enough information from the start and for that i apologize for wasting your time. I will type the question as it is on her work so you can see what i am trying to get at. the problem above was simplified from the original. "GIVEN: M is between l and n; lm=2x+1; mn=6x-3; ln = 3x^2-5 find the length of each segment. this is what i am trying to show the work for. I can see the answer just have no idea how to express the work. – Michael Cole Sep 28 '12 at 7:47
up vote 1 down vote accepted


enter image description here

You can solve the above equation using "Splitting middle term of quadratic equation" formula as well. It is mostly useful for simple equations like above.


You can re-write the above as:

$3 \cdot x^2 - 8 \cdot x -3 = 0$

Now try to express the middle term: $8 \cdot x$ as the factor of the product of the coefficient of the other two terms: $3 \cdot (-3) = (-9)$

Now $9$ can be represent as $9 \cdot 1$

Now look at the sign of the middle term: $8 \cdot x$ and it is $-$ (negetive)

Since it is negetive, express $-8x$ as $(-9x + 1x)$

So, the equation in this case will be:

$3 \cdot x^2 -9 \cdot x + 1 \cdot x -3 = 0$

$\implies (x-3)(3x+1) = 0$

$\implies x =3, -\frac{1}{3}$

Now x can't be negative.

So, $x = 3$

Now put x =3 in the above mentioned equations:


$lm = 2 \cdot x +1 = 7$

$mn = 6 \cdot x -3 = 15 $ and

$ln = 3 \cdot x^2 -5 = 22$



share|cite|improve this answer

This is a quadratic equation: the highest power of the unknown is $2$. Rearrange it to bring everything to one side of the equation:


If you can easily factor the resulting expression, you can take a shortcut, but otherwise you either complete the square or use the quadratic formula.

Completing the square relies on the fact that $(x+a)^2=x^2+2ax+a^2$. First factor out the coefficient of $x^2$:


Now notice that if you set $a=-\dfrac{8/3}2=-\dfrac43$, you’ll have $$(x+a)^2=\left(x-\frac43\right)^2=x^2-\frac83x+\frac{16}9\;,$$ which agrees in all but the constant term with the expression in parentheses in $(1)$. Thus,


and on substituting back into $(1)$ we have

$$0=3x^2-8x-3=3\left(x-\frac43\right)^2-\frac{25}3\;.$$ Rearranging this gives us

$$3\left(x-\frac43\right)^2=\frac{25}3\;,$$ or $$\left(x-\frac43\right)^2=\frac{25}9\;.$$ Finally, taking the square root on both sides and remembering that there are two square roots, one positive and one negative, we get

$$x-\frac43=\pm\frac53$$ and therefore $$x=\frac53+\frac43=\frac93=3\quad\text{or}\quad x=-\frac53+\frac43=-\frac13\;.$$

The quadratic formula can be derived by applying the method of completing the square to the general quadratic equation $ax^2+bx+c=0$. The result is that


share|cite|improve this answer

Here's a way without the formula. Using "completing the square"

\begin{align*} 3x^2-8x-3&=0\\ x^2-\frac{8}{3}x-1&=0\\ \left(x-\frac{4}{3}\right)^2-\frac{16}{9}-1&=0\\ x-\frac{4}{3}&=\pm \sqrt{\frac{25}{9}}\\ x &= \frac{4}{3}\pm \frac{5}{3}\\ x = \frac{9}{3} = 3\ \ &\mathrm{or}\ \ x = -\frac{1}{3}. \end{align*}

share|cite|improve this answer

Use the quadratic formula. First, move all the terms to one side: $8x+3=3x^2 \Rightarrow 3x^2-8x-3=0$. Then apply the formula

$\Large \hspace{60mm}x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$,

where $a=3, b=-8,$ and $c=-3$.

share|cite|improve this answer

Rewrite the equation as $3x^2-8x-3=0$ and then use the quadratic formula with $a=3,b=-8,c=-3$. $$ x=\frac{8\pm\sqrt{64+4*3*3}}{2*3} = \frac{8\pm 10}{6} = 3,-\frac{1}{3} $$

share|cite|improve this answer
2*3 = 6... not 8 – Alex Sep 28 '12 at 7:24
Sorry everyone. Made an error an forgot to check my work. It's fixed now. – chris Sep 28 '12 at 16:34

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.