32=8x^2-12x

Solution for 32=8x^2-12x equation:

32=8x^2-12x

We move all terms to the left:

32-(8x^2-12x)=0

We get rid of parentheses

-8x^2+12x+32=0

a = -8; b = 12; c = +32;
Δ = b2-4ac
Δ = 122-4·(-8)·32
Δ = 1168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{73}}{2*-8}=\frac{-12-4\sqrt{73}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{73}}{2*-8}=\frac{-12+4\sqrt{73}}{-16}
$