X*X=120+2x

Solution for X*X=120+2x equation:

X*X=120+2X

We move all terms to the left:

X*X-(120+2X)=0

We add all the numbers together, and all the variables

X*X-(2X+120)=0

Wy multiply elements

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

We get rid of parentheses

X^2-2X-120=0

a = 1; b = -2; c = -120;
Δ = b2-4ac
Δ = -22-4·1·(-120)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*1}=\frac{-20}{2}
=-10
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*1}=\frac{24}{2}
=12
$