x^2-20x=-24

Solution for x^2-20x=-24 equation:

x^2-20x=-24

We move all terms to the left:

x^2-20x-(-24)=0

We add all the numbers together, and all the variables

x^2-20x+24=0

a = 1; b = -20; c = +24;
Δ = b2-4ac
Δ = -202-4·1·24
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{19}}{2*1}=\frac{20-4\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{19}}{2*1}=\frac{20+4\sqrt{19}}{2}
$