(-5x+8)(-7x-4)=0

Solution for (-5x+8)(-7x-4)=0 equation:

(-5x+8)(-7x-4)=0

We multiply parentheses ..

(+35x^2+20x-56x-32)=0

We get rid of parentheses

35x^2+20x-56x-32=0

We add all the numbers together, and all the variables

35x^2-36x-32=0

a = 35; b = -36; c = -32;
Δ = b2-4ac
Δ = -362-4·35·(-32)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-76}{2*35}=\frac{-40}{70}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+76}{2*35}=\frac{112}{70}
=1+3/5
$