-x^2+2=X^2+16X+32

Solution for -x^2+2=X^2+16X+32 equation:

-x^2+2=x^2+16x+32

We move all terms to the left:

-x^2+2-(x^2+16x+32)=0

We add all the numbers together, and all the variables

-1x^2-(x^2+16x+32)+2=0

We get rid of parentheses

-1x^2-x^2-16x-32+2=0

We add all the numbers together, and all the variables

-2x^2-16x-30=0

a = -2; b = -16; c = -30;
Δ = b2-4ac
Δ = -162-4·(-2)·(-30)
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{-(-16)-4}{2*-2}=\frac{12}{-4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4}{2*-2}=\frac{20}{-4}
=-5
$