x^2+20x=32

Solution for x^2+20x=32 equation:

x^2+20x=32

We move all terms to the left:

x^2+20x-(32)=0

a = 1; b = 20; c = -32;
Δ = b2-4ac
Δ = 202-4·1·(-32)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{33}}{2*1}=\frac{-20-4\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{33}}{2*1}=\frac{-20+4\sqrt{33}}{2}
$