18^2+x^2=23^2

Solution for 18^2+x^2=23^2 equation:

18^2+x^2=23^2

We move all terms to the left:

18^2+x^2-(23^2)=0

We add all the numbers together, and all the variables

x^2-205=0

a = 1; b = 0; c = -205;
Δ = b2-4ac
Δ = 02-4·1·(-205)
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{205}}{2*1}=\frac{0-2\sqrt{205}}{2}
=-\frac{2\sqrt{205}}{2}
=-\sqrt{205}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{205}}{2*1}=\frac{0+2\sqrt{205}}{2}
=\frac{2\sqrt{205}}{2}
=\sqrt{205}
$