x^2-32x=-144

Solution for x^2-32x=-144 equation:

x^2-32x=-144

We move all terms to the left:

x^2-32x-(-144)=0

We add all the numbers together, and all the variables

x^2-32x+144=0

a = 1; b = -32; c = +144;
Δ = b2-4ac
Δ = -322-4·1·144
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{7}}{2*1}=\frac{32-8\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{7}}{2*1}=\frac{32+8\sqrt{7}}{2}
$