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

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

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

We multiply parentheses ..

(+24x^2+36x-4x-6)=0

We get rid of parentheses

24x^2+36x-4x-6=0

We add all the numbers together, and all the variables

24x^2+32x-6=0

a = 24; b = 32; c = -6;
Δ = b2-4ac
Δ = 322-4·24·(-6)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-40}{2*24}=\frac{-72}{48}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+40}{2*24}=\frac{8}{48}
=1/6
$