24=120x+x^2

Solution for 24=120x+x^2 equation:

24=120x+x^2

We move all terms to the left:

24-(120x+x^2)=0

We get rid of parentheses

-x^2-120x+24=0

We add all the numbers together, and all the variables

-1x^2-120x+24=0

a = -1; b = -120; c = +24;
Δ = b2-4ac
Δ = -1202-4·(-1)·24
Δ = 14496
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:

$\sqrt{\Delta}=\sqrt{14496}=\sqrt{16*906}=\sqrt{16}*\sqrt{906}=4\sqrt{906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{906}}{2*-1}=\frac{120-4\sqrt{906}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{906}}{2*-1}=\frac{120+4\sqrt{906}}{-2}
$