X(51-x)=540

Solution for X(51-x)=540 equation:

X(51-X)=540

We move all terms to the left:

X(51-X)-(540)=0

We add all the numbers together, and all the variables

X(-1X+51)-540=0

We multiply parentheses

-1X^2+51X-540=0

a = -1; b = 51; c = -540;
Δ = b2-4ac
Δ = 512-4·(-1)·(-540)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-21}{2*-1}=\frac{-72}{-2}
=+36
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+21}{2*-1}=\frac{-30}{-2}
=+15
$