a^2+a^2=16.5

Solution for a^2+a^2=16.5 equation:

a^2+a^2=16.5

We move all terms to the left:

a^2+a^2-(16.5)=0

We add all the numbers together, and all the variables

2a^2-16.5=0

a = 2; b = 0; c = -16.5;
Δ = b2-4ac
Δ = 02-4·2·(-16.5)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{33}}{2*2}=\frac{0-2\sqrt{33}}{4}
=-\frac{2\sqrt{33}}{4}
=-\frac{\sqrt{33}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{33}}{2*2}=\frac{0+2\sqrt{33}}{4}
=\frac{2\sqrt{33}}{4}
=\frac{\sqrt{33}}{2}
$