7(3x-8)(5x+1)=0

Solution for 7(3x-8)(5x+1)=0 equation:

7(3x-8)(5x+1)=0

We multiply parentheses ..

7(+15x^2+3x-40x-8)=0

We multiply parentheses

105x^2+21x-280x-56=0

We add all the numbers together, and all the variables

105x^2-259x-56=0

a = 105; b = -259; c = -56;
Δ = b2-4ac
Δ = -2592-4·105·(-56)
Δ = 90601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90601}=301$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-259)-301}{2*105}=\frac{-42}{210}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-259)+301}{2*105}=\frac{560}{210}
=2+2/3
$