10x=x^2-11

Solution for 10x=x^2-11 equation:

10x=x^2-11

We move all terms to the left:

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

We get rid of parentheses

-x^2+10x+11=0

We add all the numbers together, and all the variables

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

a = -1; b = 10; c = +11;
Δ = b2-4ac
Δ = 102-4·(-1)·11
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-12}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+12}{2*-1}=\frac{2}{-2}
=-1
$