x2-46=180

Solution for x2-46=180 equation:

x2-46=180

We move all terms to the left:

x2-46-(180)=0

We add all the numbers together, and all the variables

x^2-226=0

a = 1; b = 0; c = -226;
Δ = b2-4ac
Δ = 02-4·1·(-226)
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{226}}{2*1}=\frac{0-2\sqrt{226}}{2}
=-\frac{2\sqrt{226}}{2}
=-\sqrt{226}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{226}}{2*1}=\frac{0+2\sqrt{226}}{2}
=\frac{2\sqrt{226}}{2}
=\sqrt{226}
$