X(58-x)=816

Solution for X(58-x)=816 equation:

X(58-X)=816

We move all terms to the left:

X(58-X)-(816)=0

We add all the numbers together, and all the variables

X(-1X+58)-816=0

We multiply parentheses

-1X^2+58X-816=0

a = -1; b = 58; c = -816;
Δ = b2-4ac
Δ = 582-4·(-1)·(-816)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-10}{2*-1}=\frac{-68}{-2}
=+34
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+10}{2*-1}=\frac{-48}{-2}
=+24
$