(x)=2x^2-32

Solution for (x)=2x^2-32 equation:

(x)=2x^2-32

We move all terms to the left:

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

We get rid of parentheses

-2x^2+x+32=0

a = -2; b = 1; c = +32;
Δ = b2-4ac
Δ = 12-4·(-2)·32
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{257}}{2*-2}=\frac{-1-\sqrt{257}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{257}}{2*-2}=\frac{-1+\sqrt{257}}{-4}
$