144+400=c2

Solution for 144+400=c2 equation:

144+400=c2

We move all terms to the left:

144+400-(c2)=0

We add all the numbers together, and all the variables

-1c^2+544=0

a = -1; b = 0; c = +544;
Δ = b2-4ac
Δ = 02-4·(-1)·544
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{34}}{2*-1}=\frac{0-8\sqrt{34}}{-2}
=-\frac{8\sqrt{34}}{-2}
=-\frac{4\sqrt{34}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{34}}{2*-1}=\frac{0+8\sqrt{34}}{-2}
=\frac{8\sqrt{34}}{-2}
=\frac{4\sqrt{34}}{-1}
$