a^2+15.5^2=16^2

Solution for a^2+15.5^2=16^2 equation:

a^2+15.5^2=16^2

We move all terms to the left:

a^2+15.5^2-(16^2)=0

We add all the numbers together, and all the variables

a^2-15.75=0

a = 1; b = 0; c = -15.75;
Δ = b2-4ac
Δ = 02-4·1·(-15.75)
Δ = 63
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{63}=\sqrt{9*7}=\sqrt{9}*\sqrt{7}=3\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{7}}{2*1}=\frac{0-3\sqrt{7}}{2}
=-\frac{3\sqrt{7}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{7}}{2*1}=\frac{0+3\sqrt{7}}{2}
=\frac{3\sqrt{7}}{2}
$