11.5^2+x^2=20^2

Solution for 11.5^2+x^2=20^2 equation:

11.5^2+x^2=20^2

We move all terms to the left:

11.5^2+x^2-(20^2)=0

We add all the numbers together, and all the variables

x^2-267.75=0

a = 1; b = 0; c = -267.75;
Δ = b2-4ac
Δ = 02-4·1·(-267.75)
Δ = 1071
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:

$\sqrt{\Delta}=\sqrt{1071}=\sqrt{9*119}=\sqrt{9}*\sqrt{119}=3\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{119}}{2*1}=\frac{0-3\sqrt{119}}{2}
=-\frac{3\sqrt{119}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{119}}{2*1}=\frac{0+3\sqrt{119}}{2}
=\frac{3\sqrt{119}}{2}
$