10x-(x-11)=x2

Solution for 10x-(x-11)=x2 equation:

10x-(x-11)=x2

We move all terms to the left:

10x-(x-11)-(x2)=0

We add all the numbers together, and all the variables

-1x^2+10x-(x-11)=0

We get rid of parentheses

-1x^2+10x-x+11=0

We add all the numbers together, and all the variables

-1x^2+9x+11=0

a = -1; b = 9; c = +11;
Δ = b2-4ac
Δ = 92-4·(-1)·11
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5\sqrt{5}}{2*-1}=\frac{-9-5\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5\sqrt{5}}{2*-1}=\frac{-9+5\sqrt{5}}{-2}
$