4(7x-5)(3x+1)=0

Solution for 4(7x-5)(3x+1)=0 equation:

4(7x-5)(3x+1)=0

We multiply parentheses ..

4(+21x^2+7x-15x-5)=0

We multiply parentheses

84x^2+28x-60x-20=0

We add all the numbers together, and all the variables

84x^2-32x-20=0

a = 84; b = -32; c = -20;
Δ = b2-4ac
Δ = -322-4·84·(-20)
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-88}{2*84}=\frac{-56}{168}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+88}{2*84}=\frac{120}{168}
=5/7
$