X(84-x)=180

Solution for X(84-x)=180 equation:

X(84-X)=180

We move all terms to the left:

X(84-X)-(180)=0

We add all the numbers together, and all the variables

X(-1X+84)-180=0

We multiply parentheses

-1X^2+84X-180=0

a = -1; b = 84; c = -180;
Δ = b2-4ac
Δ = 842-4·(-1)·(-180)
Δ = 6336
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:

$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-24\sqrt{11}}{2*-1}=\frac{-84-24\sqrt{11}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+24\sqrt{11}}{2*-1}=\frac{-84+24\sqrt{11}}{-2}
$