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

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

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

We multiply parentheses

7x^2+35x+(x+5)=0

We get rid of parentheses

7x^2+35x+x+5=0

We add all the numbers together, and all the variables

7x^2+36x+5=0

a = 7; b = 36; c = +5;
Δ = b2-4ac
Δ = 362-4·7·5
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-34}{2*7}=\frac{-70}{14}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+34}{2*7}=\frac{-2}{14}
=-1/7
$