(X-9)(x-15)=0

Solution for (X-9)(x-15)=0 equation:

(X-9)(X-15)=0

We multiply parentheses ..

(+X^2-15X-9X+135)=0

We get rid of parentheses

X^2-15X-9X+135=0

We add all the numbers together, and all the variables

X^2-24X+135=0

a = 1; b = -24; c = +135;
Δ = b2-4ac
Δ = -242-4·1·135
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6}{2*1}=\frac{18}{2}
=9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6}{2*1}=\frac{30}{2}
=15
$