(x-3)(x-15)=0

Solution for (x-3)(x-15)=0 equation:

(x-3)(x-15)=0

We multiply parentheses ..

(+x^2-15x-3x+45)=0

We get rid of parentheses

x^2-15x-3x+45=0

We add all the numbers together, and all the variables

x^2-18x+45=0

a = 1; b = -18; c = +45;
Δ = b2-4ac
Δ = -182-4·1·45
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12}{2*1}=\frac{30}{2}
=15
$