X(18-X)-72=o

Solution for X(18-X)-72=o equation:

X(18-X)-72=X

We move all terms to the left:

X(18-X)-72-(X)=0

We add all the numbers together, and all the variables

X(-1X+18)-X-72=0

We add all the numbers together, and all the variables

-1X+X(-1X+18)-72=0

We multiply parentheses

-1X^2-1X+18X-72=0

We add all the numbers together, and all the variables

-1X^2+17X-72=0

a = -1; b = 17; c = -72;
Δ = b2-4ac
Δ = 172-4·(-1)·(-72)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-1}{2*-1}=\frac{-18}{-2}
=+9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+1}{2*-1}=\frac{-16}{-2}
=+8
$