(8x-5)(4x+12)=0

Solution for (8x-5)(4x+12)=0 equation:

(8x-5)(4x+12)=0

We multiply parentheses ..

(+32x^2+96x-20x-60)=0

We get rid of parentheses

32x^2+96x-20x-60=0

We add all the numbers together, and all the variables

32x^2+76x-60=0

a = 32; b = 76; c = -60;
Δ = b2-4ac
Δ = 762-4·32·(-60)
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-116}{2*32}=\frac{-192}{64}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+116}{2*32}=\frac{40}{64}
=5/8
$