X2-1=x+6

Solution for X2-1=x+6 equation:

X2-1=X+6

We move all terms to the left:

X2-1-(X+6)=0

We add all the numbers together, and all the variables

X^2-(X+6)-1=0

We get rid of parentheses

X^2-X-6-1=0

We add all the numbers together, and all the variables

X^2-1X-7=0

a = 1; b = -1; c = -7;
Δ = b2-4ac
Δ = -12-4·1·(-7)
Δ = 29
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{29}}{2*1}=\frac{1-\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{29}}{2*1}=\frac{1+\sqrt{29}}{2}
$