a^2-513-46656=0

Solution for a^2-513-46656=0 equation:

a^2-513-46656=0

We add all the numbers together, and all the variables

a^2-47169=0

a = 1; b = 0; c = -47169;
Δ = b2-4ac
Δ = 02-4·1·(-47169)
Δ = 188676
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:

$\sqrt{\Delta}=\sqrt{188676}=\sqrt{36*5241}=\sqrt{36}*\sqrt{5241}=6\sqrt{5241}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5241}}{2*1}=\frac{0-6\sqrt{5241}}{2}
=-\frac{6\sqrt{5241}}{2}
=-3\sqrt{5241}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5241}}{2*1}=\frac{0+6\sqrt{5241}}{2}
=\frac{6\sqrt{5241}}{2}
=3\sqrt{5241}
$