X2-(x-1)2=2-x2

Solution for X2-(x-1)2=2-x2 equation:

X2-(X-1)2=2-X2

We move all terms to the left:

X2-(X-1)2-(2-X2)=0

We add all the numbers together, and all the variables

-(-1X^2+2)+X2-(X-1)2=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

X^2+1X^2-2X-2+2=0

We add all the numbers together, and all the variables

2X^2-2X=0

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

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