4(5-7x)(8x+1)=0

Solution for 4(5-7x)(8x+1)=0 equation:

4(5-7x)(8x+1)=0

We add all the numbers together, and all the variables

4(-7x+5)(8x+1)=0

We multiply parentheses ..

4(-56x^2-7x+40x+5)=0

We multiply parentheses

-224x^2-28x+160x+20=0

We add all the numbers together, and all the variables

-224x^2+132x+20=0

a = -224; b = 132; c = +20;
Δ = b2-4ac
Δ = 1322-4·(-224)·20
Δ = 35344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35344}=188$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-188}{2*-224}=\frac{-320}{-448}
=5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+188}{2*-224}=\frac{56}{-448}
=-1/8
$