(c-1)(c-1)=1

Solution for (c-1)(c-1)=1 equation:

(c-1)(c-1)=1

We move all terms to the left:

(c-1)(c-1)-(1)=0

We multiply parentheses ..

(+c^2-1c-1c+1)-1=0

We get rid of parentheses

c^2-1c-1c+1-1=0

We add all the numbers together, and all the variables

c^2-2c=0

a = 1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·1·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*1}=\frac{0}{2}
=0
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*1}=\frac{4}{2}
=2
$