(3x-15)(12x-3)=0

Solution for (3x-15)(12x-3)=0 equation:

(3x-15)(12x-3)=0

We multiply parentheses ..

(+36x^2-9x-180x+45)=0

We get rid of parentheses

36x^2-9x-180x+45=0

We add all the numbers together, and all the variables

36x^2-189x+45=0

a = 36; b = -189; c = +45;
Δ = b2-4ac
Δ = -1892-4·36·45
Δ = 29241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29241}=171$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-171}{2*36}=\frac{18}{72}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+171}{2*36}=\frac{360}{72}
=5
$