-7x(x+2)=x+2

Solution for -7x(x+2)=x+2 equation:

-7x(x+2)=x+2

We move all terms to the left:

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

We multiply parentheses

-7x^2-14x-(x+2)=0

We get rid of parentheses

-7x^2-14x-x-2=0

We add all the numbers together, and all the variables

-7x^2-15x-2=0

a = -7; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·(-7)·(-2)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-13}{2*-7}=\frac{2}{-14}
=-1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+13}{2*-7}=\frac{28}{-14}
=-2
$