(x+32)(x)=90

Solution for (x+32)(x)=90 equation:

(x+32)(x)=90

We move all terms to the left:

(x+32)(x)-(90)=0

We multiply parentheses

x^2+32x-90=0

a = 1; b = 32; c = -90;
Δ = b2-4ac
Δ = 322-4·1·(-90)
Δ = 1384
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:

$\sqrt{\Delta}=\sqrt{1384}=\sqrt{4*346}=\sqrt{4}*\sqrt{346}=2\sqrt{346}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-2\sqrt{346}}{2*1}=\frac{-32-2\sqrt{346}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+2\sqrt{346}}{2*1}=\frac{-32+2\sqrt{346}}{2}
$