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

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

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

We multiply parentheses ..

(+5x^2-1x+5x-1)=0

We get rid of parentheses

5x^2-1x+5x-1=0

We add all the numbers together, and all the variables

5x^2+4x-1=0

a = 5; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·5·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6}{2*5}=\frac{2}{10}
=1/5
$