We can solve the equation $12x^2-5x-3>0$ with the pq-formula, but I think this is very error-prone without a calculator. Now I find a simpler way to solve it. I rewrite the equation as $(3x+1)(4x-3)>0$. Then I solve both multiplicands for $x$:
It seems to work. But the right result is
$x<-1/3$ : Here the inequality is reversed. Why? Where is my mistake?
$x>3/4$ : That's right.