(1-x)(1-x)=8

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

(1-x)(1-x)=8

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-2x-7=0

a = 1; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·1·(-7)
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{-(-2)-4\sqrt{2}}{2*1}=\frac{2-4\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{2}}{2*1}=\frac{2+4\sqrt{2}}{2}
$