(2x-6)(3x-1)=0

Solution for (2x-6)(3x-1)=0 equation:

(2x-6)(3x-1)=0

We multiply parentheses ..

(+6x^2-2x-18x+6)=0

We get rid of parentheses

6x^2-2x-18x+6=0

We add all the numbers together, and all the variables

6x^2-20x+6=0

a = 6; b = -20; c = +6;
Δ = b2-4ac
Δ = -202-4·6·6
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16}{2*6}=\frac{4}{12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16}{2*6}=\frac{36}{12}
=3
$