(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+9x-2=0

a = 18; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·18·(-2)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*18}=\frac{-24}{36}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*18}=\frac{6}{36}
=1/6
$