2x^2-11x-11=x+4

Solution for 2x^2-11x-11=x+4 equation:

2x^2-11x-11=x+4

We move all terms to the left:

2x^2-11x-11-(x+4)=0

We get rid of parentheses

2x^2-11x-x-4-11=0

We add all the numbers together, and all the variables

2x^2-12x-15=0

a = 2; b = -12; c = -15;
Δ = b2-4ac
Δ = -122-4·2·(-15)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*2}=\frac{12-2\sqrt{66}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*2}=\frac{12+2\sqrt{66}}{4}
$