27-x^2=2^2

Solution for 27-x^2=2^2 equation:

27-x^2=2^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x^2+23=0

a = -1; b = 0; c = +23;
Δ = b2-4ac
Δ = 02-4·(-1)·23
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{23}}{2*-1}=\frac{0-2\sqrt{23}}{-2}
=-\frac{2\sqrt{23}}{-2}
=-\frac{\sqrt{23}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{23}}{2*-1}=\frac{0+2\sqrt{23}}{-2}
=\frac{2\sqrt{23}}{-2}
=\frac{\sqrt{23}}{-1}
$