a^2+64=607

Solution for a^2+64=607 equation:

a^2+64=607

We move all terms to the left:

a^2+64-(607)=0

We add all the numbers together, and all the variables

a^2-543=0

a = 1; b = 0; c = -543;
Δ = b2-4ac
Δ = 02-4·1·(-543)
Δ = 2172
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:

$\sqrt{\Delta}=\sqrt{2172}=\sqrt{4*543}=\sqrt{4}*\sqrt{543}=2\sqrt{543}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{543}}{2*1}=\frac{0-2\sqrt{543}}{2}
=-\frac{2\sqrt{543}}{2}
=-\sqrt{543}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{543}}{2*1}=\frac{0+2\sqrt{543}}{2}
=\frac{2\sqrt{543}}{2}
=\sqrt{543}
$