(4x-1)(6x+6)=0

Solution for (4x-1)(6x+6)=0 equation:

(4x-1)(6x+6)=0

We multiply parentheses ..

(+24x^2+24x-6x-6)=0

We get rid of parentheses

24x^2+24x-6x-6=0

We add all the numbers together, and all the variables

24x^2+18x-6=0

a = 24; b = 18; c = -6;
Δ = b2-4ac
Δ = 182-4·24·(-6)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*24}=\frac{-48}{48}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*24}=\frac{12}{48}
=1/4
$