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+48x+140=0

a = 4; b = 48; c = +140;
Δ = b2-4ac
Δ = 482-4·4·140
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8}{2*4}=\frac{-56}{8}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8}{2*4}=\frac{-40}{8}
=-5
$