a^2+a^2=56.25

Solution for a^2+a^2=56.25 equation:

a^2+a^2=56.25

We move all terms to the left:

a^2+a^2-(56.25)=0

We add all the numbers together, and all the variables

2a^2-56.25=0

a = 2; b = 0; c = -56.25;
Δ = b2-4ac
Δ = 02-4·2·(-56.25)
Δ = 450
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:

$\sqrt{\Delta}=\sqrt{450}=\sqrt{225*2}=\sqrt{225}*\sqrt{2}=15\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-15\sqrt{2}}{2*2}=\frac{0-15\sqrt{2}}{4}
=-\frac{15\sqrt{2}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+15\sqrt{2}}{2*2}=\frac{0+15\sqrt{2}}{4}
=\frac{15\sqrt{2}}{4}
$