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

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

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

We multiply parentheses ..

4(+x^2-5x+7x-35)=0

We multiply parentheses

4x^2-20x+28x-140=0

We add all the numbers together, and all the variables

4x^2+8x-140=0

a = 4; b = 8; c = -140;
Δ = b2-4ac
Δ = 82-4·4·(-140)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-48}{2*4}=\frac{-56}{8}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+48}{2*4}=\frac{40}{8}
=5
$