5x+120=x^2-12x

Solution for 5x+120=x^2-12x equation:

5x+120=x^2-12x

We move all terms to the left:

5x+120-(x^2-12x)=0

We get rid of parentheses

-x^2+5x+12x+120=0

We add all the numbers together, and all the variables

-1x^2+17x+120=0

a = -1; b = 17; c = +120;
Δ = b2-4ac
Δ = 172-4·(-1)·120
Δ = 769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{769}}{2*-1}=\frac{-17-\sqrt{769}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{769}}{2*-1}=\frac{-17+\sqrt{769}}{-2}
$