X^2-92=-20x

Solution for X^2-92=-20x equation:

X^2-92=-20X

We move all terms to the left:

X^2-92-(-20X)=0

We get rid of parentheses

X^2+20X-92=0

a = 1; b = 20; c = -92;
Δ = b2-4ac
Δ = 202-4·1·(-92)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-16\sqrt{3}}{2*1}=\frac{-20-16\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+16\sqrt{3}}{2*1}=\frac{-20+16\sqrt{3}}{2}
$