x2-6=180

Solution for x2-6=180 equation:

x2-6=180

We move all terms to the left:

x2-6-(180)=0

We add all the numbers together, and all the variables

x^2-186=0

a = 1; b = 0; c = -186;
Δ = b2-4ac
Δ = 02-4·1·(-186)
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{186}}{2*1}=\frac{0-2\sqrt{186}}{2}
=-\frac{2\sqrt{186}}{2}
=-\sqrt{186}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{186}}{2*1}=\frac{0+2\sqrt{186}}{2}
=\frac{2\sqrt{186}}{2}
=\sqrt{186}
$