X(15-x)=38

Solution for X(15-x)=38 equation:

X(15-X)=38

We move all terms to the left:

X(15-X)-(38)=0

We add all the numbers together, and all the variables

X(-1X+15)-38=0

We multiply parentheses

-1X^2+15X-38=0

a = -1; b = 15; c = -38;
Δ = b2-4ac
Δ = 152-4·(-1)·(-38)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{73}}{2*-1}=\frac{-15-\sqrt{73}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{73}}{2*-1}=\frac{-15+\sqrt{73}}{-2}
$