x^2-4x+1=2x+6

Solution for x^2-4x+1=2x+6 equation:

x^2-4x+1=2x+6

We move all terms to the left:

x^2-4x+1-(2x+6)=0

We get rid of parentheses

x^2-4x-2x-6+1=0

We add all the numbers together, and all the variables

x^2-6x-5=0

a = 1; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·1·(-5)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{14}}{2*1}=\frac{6-2\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{14}}{2*1}=\frac{6+2\sqrt{14}}{2}
$