X^2-6x=8+x

Solution for X^2-6x=8+x equation:

X^2-6X=8+X

We move all terms to the left:

X^2-6X-(8+X)=0

We add all the numbers together, and all the variables

X^2-6X-(X+8)=0

We get rid of parentheses

X^2-6X-X-8=0

We add all the numbers together, and all the variables

X^2-7X-8=0

a = 1; b = -7; c = -8;
Δ = b2-4ac
Δ = -72-4·1·(-8)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*1}=\frac{16}{2}
=8
$