(8x-3)(5x+120)=0

Solution for (8x-3)(5x+120)=0 equation:

(8x-3)(5x+120)=0

We multiply parentheses ..

(+40x^2+960x-15x-360)=0

We get rid of parentheses

40x^2+960x-15x-360=0

We add all the numbers together, and all the variables

40x^2+945x-360=0

a = 40; b = 945; c = -360;
Δ = b2-4ac
Δ = 9452-4·40·(-360)
Δ = 950625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{950625}=975$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(945)-975}{2*40}=\frac{-1920}{80}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(945)+975}{2*40}=\frac{30}{80}
=3/8
$