a^2+6a^2=13^2

Solution for a^2+6a^2=13^2 equation:

a^2+6a^2=13^2

We move all terms to the left:

a^2+6a^2-(13^2)=0

We add all the numbers together, and all the variables

7a^2-169=0

a = 7; b = 0; c = -169;
Δ = b2-4ac
Δ = 02-4·7·(-169)
Δ = 4732
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:

$\sqrt{\Delta}=\sqrt{4732}=\sqrt{676*7}=\sqrt{676}*\sqrt{7}=26\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-26\sqrt{7}}{2*7}=\frac{0-26\sqrt{7}}{14}
=-\frac{26\sqrt{7}}{14}
=-\frac{13\sqrt{7}}{7}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+26\sqrt{7}}{2*7}=\frac{0+26\sqrt{7}}{14}
=\frac{26\sqrt{7}}{14}
=\frac{13\sqrt{7}}{7}
$