(3x+15)(4x-8)=0

Solution for (3x+15)(4x-8)=0 equation:

(3x+15)(4x-8)=0

We multiply parentheses ..

(+12x^2-24x+60x-120)=0

We get rid of parentheses

12x^2-24x+60x-120=0

We add all the numbers together, and all the variables

12x^2+36x-120=0

a = 12; b = 36; c = -120;
Δ = b2-4ac
Δ = 362-4·12·(-120)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-84}{2*12}=\frac{-120}{24}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+84}{2*12}=\frac{48}{24}
=2
$