(X-2)2-(x+1)(x-1)=5

Solution for (X-2)2-(x+1)(x-1)=5 equation:

(X-2)2-(X+1)(X-1)=5

We move all terms to the left:

(X-2)2-(X+1)(X-1)-(5)=0

We use the square of the difference formula

X^2+(X-2)2+1-5=0

We multiply parentheses

X^2+2X-4+1-5=0

We add all the numbers together, and all the variables

X^2+2X-8=0

a = 1; b = 2; c = -8;
Δ = b2-4ac
Δ = 22-4·1·(-8)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*1}=\frac{-8}{2}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*1}=\frac{4}{2}
=2
$