(x+1)(x+1)=8x

Solution for (x+1)(x+1)=8x equation:

(x+1)(x+1)=8x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-6x+1=0

a = 1; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·1·1
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{2}}{2*1}=\frac{6-4\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{2}}{2*1}=\frac{6+4\sqrt{2}}{2}
$