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

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

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

We multiply parentheses ..

(+7x^2+4x-49x-28)=0

We get rid of parentheses

7x^2+4x-49x-28=0

We add all the numbers together, and all the variables

7x^2-45x-28=0

a = 7; b = -45; c = -28;
Δ = b2-4ac
Δ = -452-4·7·(-28)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-53}{2*7}=\frac{-8}{14}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+53}{2*7}=\frac{98}{14}
=7
$