11=x2-27

Solution for 11=x2-27 equation:

11=x2-27

We move all terms to the left:

11-(x2-27)=0

We add all the numbers together, and all the variables

-(+x^2-27)+11=0

We get rid of parentheses

-x^2+27+11=0

We add all the numbers together, and all the variables

-1x^2+38=0

a = -1; b = 0; c = +38;
Δ = b2-4ac
Δ = 02-4·(-1)·38
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{38}}{2*-1}=\frac{0-2\sqrt{38}}{-2}
=-\frac{2\sqrt{38}}{-2}
=-\frac{\sqrt{38}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{38}}{2*-1}=\frac{0+2\sqrt{38}}{-2}
=\frac{2\sqrt{38}}{-2}
=\frac{\sqrt{38}}{-1}
$