c^2=5128

Solution for c^2=5128 equation:

c^2=5128

We move all terms to the left:

c^2-(5128)=0

a = 1; b = 0; c = -5128;
Δ = b2-4ac
Δ = 02-4·1·(-5128)
Δ = 20512
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20512}=\sqrt{16*1282}=\sqrt{16}*\sqrt{1282}=4\sqrt{1282}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1282}}{2*1}=\frac{0-4\sqrt{1282}}{2}
=-\frac{4\sqrt{1282}}{2}
=-2\sqrt{1282}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1282}}{2*1}=\frac{0+4\sqrt{1282}}{2}
=\frac{4\sqrt{1282}}{2}
=2\sqrt{1282}
$