c2=169144

Solution for c2=169144 equation:

c2=169144

We move all terms to the left:

c2-(169144)=0

We add all the numbers together, and all the variables

c^2-169144=0

a = 1; b = 0; c = -169144;
Δ = b2-4ac
Δ = 02-4·1·(-169144)
Δ = 676576
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:

$\sqrt{\Delta}=\sqrt{676576}=\sqrt{16*42286}=\sqrt{16}*\sqrt{42286}=4\sqrt{42286}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42286}}{2*1}=\frac{0-4\sqrt{42286}}{2}
=-\frac{4\sqrt{42286}}{2}
=-2\sqrt{42286}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42286}}{2*1}=\frac{0+4\sqrt{42286}}{2}
=\frac{4\sqrt{42286}}{2}
=2\sqrt{42286}
$