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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2+16x-3=0

a = 12; b = 16; c = -3;
Δ = b2-4ac
Δ = 162-4·12·(-3)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*12}=\frac{4}{24}
=1/6
$