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

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

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

We multiply parentheses ..

(+18x^2-12x-3x+2)=0

We get rid of parentheses

18x^2-12x-3x+2=0

We add all the numbers together, and all the variables

18x^2-15x+2=0

a = 18; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·18·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*18}=\frac{6}{36}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*18}=\frac{24}{36}
=2/3
$