3x+108=x^2-2x

Solution for 3x+108=x^2-2x equation:

3x+108=x^2-2x

We move all terms to the left:

3x+108-(x^2-2x)=0

We get rid of parentheses

-x^2+3x+2x+108=0

We add all the numbers together, and all the variables

-1x^2+5x+108=0

a = -1; b = 5; c = +108;
Δ = b2-4ac
Δ = 52-4·(-1)·108
Δ = 457
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{-(5)-\sqrt{457}}{2*-1}=\frac{-5-\sqrt{457}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{457}}{2*-1}=\frac{-5+\sqrt{457}}{-2}
$