x^2-6x+1=2x+8

Solution for x^2-6x+1=2x+8 equation:

x^2-6x+1=2x+8

We move all terms to the left:

x^2-6x+1-(2x+8)=0

We get rid of parentheses

x^2-6x-2x-8+1=0

We add all the numbers together, and all the variables

x^2-8x-7=0

a = 1; b = -8; c = -7;
Δ = b2-4ac
Δ = -82-4·1·(-7)
Δ = 92
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{23}}{2*1}=\frac{8-2\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{23}}{2*1}=\frac{8+2\sqrt{23}}{2}
$