(6x-8)(2x+12)=0

Solution for (6x-8)(2x+12)=0 equation:

(6x-8)(2x+12)=0

We multiply parentheses ..

(+12x^2+72x-16x-96)=0

We get rid of parentheses

12x^2+72x-16x-96=0

We add all the numbers together, and all the variables

12x^2+56x-96=0

a = 12; b = 56; c = -96;
Δ = b2-4ac
Δ = 562-4·12·(-96)
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-88}{2*12}=\frac{-144}{24}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+88}{2*12}=\frac{32}{24}
=1+1/3
$