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

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

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

We multiply parentheses ..

(+35x^2-49x+40x-56)=0

We get rid of parentheses

35x^2-49x+40x-56=0

We add all the numbers together, and all the variables

35x^2-9x-56=0

a = 35; b = -9; c = -56;
Δ = b2-4ac
Δ = -92-4·35·(-56)
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-89}{2*35}=\frac{-80}{70}
=-1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+89}{2*35}=\frac{98}{70}
=1+2/5
$