x(x+7)=x+7

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

x(x+7)=x+7

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

x^2+7x-x-7=0

We add all the numbers together, and all the variables

x^2+6x-7=0

a = 1; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·1·(-7)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8}{2*1}=\frac{2}{2}
=1
$