X2-6=x+2

Solution for X2-6=x+2 equation:

X2-6=X+2

We move all terms to the left:

X2-6-(X+2)=0

We add all the numbers together, and all the variables

X^2-(X+2)-6=0

We get rid of parentheses

X^2-X-2-6=0

We add all the numbers together, and all the variables

X^2-1X-8=0

a = 1; b = -1; c = -8;
Δ = b2-4ac
Δ = -12-4·1·(-8)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{33}}{2*1}=\frac{1-\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*1}=\frac{1+\sqrt{33}}{2}
$