(4x-12)(8x+3)=0

Solution for (4x-12)(8x+3)=0 equation:

(4x-12)(8x+3)=0

We multiply parentheses ..

(+32x^2+12x-96x-36)=0

We get rid of parentheses

32x^2+12x-96x-36=0

We add all the numbers together, and all the variables

32x^2-84x-36=0

a = 32; b = -84; c = -36;
Δ = b2-4ac
Δ = -842-4·32·(-36)
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-108}{2*32}=\frac{-24}{64}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+108}{2*32}=\frac{192}{64}
=3
$