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

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

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

We multiply parentheses ..

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

We multiply parentheses

5x^2-35x+5x-35=0

We add all the numbers together, and all the variables

5x^2-30x-35=0

a = 5; b = -30; c = -35;
Δ = b2-4ac
Δ = -302-4·5·(-35)
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{-(-30)-40}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+40}{2*5}=\frac{70}{10}
=7
$