X^2-20x=320

Solution for X^2-20x=320 equation:

X^2-20X=320

We move all terms to the left:

X^2-20X-(320)=0

a = 1; b = -20; c = -320;
Δ = b2-4ac
Δ = -202-4·1·(-320)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{105}}{2*1}=\frac{20-4\sqrt{105}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{105}}{2*1}=\frac{20+4\sqrt{105}}{2}
$