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

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

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

We multiply parentheses ..

4(+x^2+7x-3x-21)=0

We multiply parentheses

4x^2+28x-12x-84=0

We add all the numbers together, and all the variables

4x^2+16x-84=0

a = 4; b = 16; c = -84;
Δ = b2-4ac
Δ = 162-4·4·(-84)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-40}{2*4}=\frac{-56}{8}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+40}{2*4}=\frac{24}{8}
=3
$