(5x+7)(3x-8)=0

Solution for (5x+7)(3x-8)=0 equation:

(5x+7)(3x-8)=0

We multiply parentheses ..

(+15x^2-40x+21x-56)=0

We get rid of parentheses

15x^2-40x+21x-56=0

We add all the numbers together, and all the variables

15x^2-19x-56=0

a = 15; b = -19; c = -56;
Δ = b2-4ac
Δ = -192-4·15·(-56)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-61}{2*15}=\frac{-42}{30}
=-1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+61}{2*15}=\frac{80}{30}
=2+2/3
$