a^2+(6a)^2=7^2

Solution for a^2+(6a)^2=7^2 equation:

a^2+(6a)^2=7^2

We move all terms to the left:

a^2+(6a)^2-(7^2)=0

We add all the numbers together, and all the variables

7a^2-49=0

a = 7; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·7·(-49)
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{7}}{2*7}=\frac{0-14\sqrt{7}}{14}
=-\frac{14\sqrt{7}}{14}
=-\sqrt{7}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{7}}{2*7}=\frac{0+14\sqrt{7}}{14}
=\frac{14\sqrt{7}}{14}
=\sqrt{7}
$