X^2-120=-4x

Solution for X^2-120=-4x equation:

X^2-120=-4X

We move all terms to the left:

X^2-120-(-4X)=0

We get rid of parentheses

X^2+4X-120=0

a = 1; b = 4; c = -120;
Δ = b2-4ac
Δ = 42-4·1·(-120)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{31}}{2*1}=\frac{-4-4\sqrt{31}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{31}}{2*1}=\frac{-4+4\sqrt{31}}{2}
$