120-2x=x^2-18x+84

Solution for 120-2x=x^2-18x+84 equation:

120-2x=x^2-18x+84

We move all terms to the left:

120-2x-(x^2-18x+84)=0

We get rid of parentheses

-x^2-2x+18x-84+120=0

We add all the numbers together, and all the variables

-1x^2+16x+36=0

a = -1; b = 16; c = +36;
Δ = b2-4ac
Δ = 162-4·(-1)·36
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*-1}=\frac{-36}{-2}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*-1}=\frac{4}{-2}
=-2
$