5.5^2+x^2=30.5^2

Solution for 5.5^2+x^2=30.5^2 equation:

5.5^2+x^2=30.5^2

We move all terms to the left:

5.5^2+x^2-(30.5^2)=0

We add all the numbers together, and all the variables

x^2-900=0

a = 1; b = 0; c = -900;
Δ = b2-4ac
Δ = 02-4·1·(-900)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*1}=\frac{60}{2}
=30
$