X(30-x)=81

Solution for X(30-x)=81 equation:

X(30-X)=81

We move all terms to the left:

X(30-X)-(81)=0

We add all the numbers together, and all the variables

X(-1X+30)-81=0

We multiply parentheses

-1X^2+30X-81=0

a = -1; b = 30; c = -81;
Δ = b2-4ac
Δ = 302-4·(-1)·(-81)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-24}{2*-1}=\frac{-54}{-2}
=+27
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+24}{2*-1}=\frac{-6}{-2}
=+3
$