32x-124=2x2+2

Solution for 32x-124=2x2+2 equation:

32x-124=2x^2+2

We move all terms to the left:

32x-124-(2x^2+2)=0

We get rid of parentheses

-2x^2+32x-2-124=0

We add all the numbers together, and all the variables

-2x^2+32x-126=0

a = -2; b = 32; c = -126;
Δ = b2-4ac
Δ = 322-4·(-2)·(-126)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4}{2*-2}=\frac{-36}{-4}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4}{2*-2}=\frac{-28}{-4}
=+7
$