c2+96=180

Solution for c2+96=180 equation:

c2+96=180

We move all terms to the left:

c2+96-(180)=0

We add all the numbers together, and all the variables

c^2-84=0

a = 1; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·1·(-84)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*1}=\frac{0-4\sqrt{21}}{2}
=-\frac{4\sqrt{21}}{2}
=-2\sqrt{21}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*1}=\frac{0+4\sqrt{21}}{2}
=\frac{4\sqrt{21}}{2}
=2\sqrt{21}
$