(3x-6)(5x-1)=0

Solution for (3x-6)(5x-1)=0 equation:

(3x-6)(5x-1)=0

We multiply parentheses ..

(+15x^2-3x-30x+6)=0

We get rid of parentheses

15x^2-3x-30x+6=0

We add all the numbers together, and all the variables

15x^2-33x+6=0

a = 15; b = -33; c = +6;
Δ = b2-4ac
Δ = -332-4·15·6
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-27}{2*15}=\frac{6}{30}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+27}{2*15}=\frac{60}{30}
=2
$