(x^2-2x+6)-(2x+11)=x

Solution for (x^2-2x+6)-(2x+11)=x equation:

(x^2-2x+6)-(2x+11)=x

We move all terms to the left:

(x^2-2x+6)-(2x+11)-(x)=0

We add all the numbers together, and all the variables

-1x+(x^2-2x+6)-(2x+11)=0

We get rid of parentheses

x^2-1x-2x-2x+6-11=0

We add all the numbers together, and all the variables

x^2-5x-5=0

a = 1; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·1·(-5)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{5}}{2*1}=\frac{5-3\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{5}}{2*1}=\frac{5+3\sqrt{5}}{2}
$