a^2+a^2=89

Solution for a^2+a^2=89 equation:

a^2+a^2=89

We move all terms to the left:

a^2+a^2-(89)=0

We add all the numbers together, and all the variables

2a^2-89=0

a = 2; b = 0; c = -89;
Δ = b2-4ac
Δ = 02-4·2·(-89)
Δ = 712
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:

$\sqrt{\Delta}=\sqrt{712}=\sqrt{4*178}=\sqrt{4}*\sqrt{178}=2\sqrt{178}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{178}}{2*2}=\frac{0-2\sqrt{178}}{4}
=-\frac{2\sqrt{178}}{4}
=-\frac{\sqrt{178}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{178}}{2*2}=\frac{0+2\sqrt{178}}{4}
=\frac{2\sqrt{178}}{4}
=\frac{\sqrt{178}}{2}
$