(x+8)(x+2)=x

Solution for (x+8)(x+2)=x equation:

(x+8)(x+2)=x

We move all terms to the left:

(x+8)(x+2)-(x)=0

We add all the numbers together, and all the variables

-1x+(x+8)(x+2)=0

We multiply parentheses ..

(+x^2+2x+8x+16)-1x=0

We get rid of parentheses

x^2+2x+8x-1x+16=0

We add all the numbers together, and all the variables

x^2+9x+16=0

a = 1; b = 9; c = +16;
Δ = b2-4ac
Δ = 92-4·1·16
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{17}}{2*1}=\frac{-9-\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{17}}{2*1}=\frac{-9+\sqrt{17}}{2}
$