h^2=121-5.5^2

Solution for h^2=121-5.5^2 equation:

h^2=121-5.5^2

We move all terms to the left:

h^2-(121-5.5^2)=0

We add all the numbers together, and all the variables

h^2-90.75=0

a = 1; b = 0; c = -90.75;
Δ = b2-4ac
Δ = 02-4·1·(-90.75)
Δ = 363
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{363}=\sqrt{121*3}=\sqrt{121}*\sqrt{3}=11\sqrt{3}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-11\sqrt{3}}{2*1}=\frac{0-11\sqrt{3}}{2}
=-\frac{11\sqrt{3}}{2}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+11\sqrt{3}}{2*1}=\frac{0+11\sqrt{3}}{2}
=\frac{11\sqrt{3}}{2}
$