x^2+32=-18x

Solution for x^2+32=-18x equation:

x^2+32=-18x

We move all terms to the left:

x^2+32-(-18x)=0

We get rid of parentheses

x^2+18x+32=0

a = 1; b = 18; c = +32;
Δ = b2-4ac
Δ = 182-4·1·32
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-14}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+14}{2*1}=\frac{-4}{2}
=-2
$