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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2+6x+1=0

a = 5; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·5·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4}{2*5}=\frac{-2}{10}
=-1/5
$