c2=111

Solution for c2=111 equation:

c2=111

We move all terms to the left:

c2-(111)=0

We add all the numbers together, and all the variables

c^2-111=0

a = 1; b = 0; c = -111;
Δ = b2-4ac
Δ = 02-4·1·(-111)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{111}}{2*1}=\frac{0-2\sqrt{111}}{2}
=-\frac{2\sqrt{111}}{2}
=-\sqrt{111}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{111}}{2*1}=\frac{0+2\sqrt{111}}{2}
=\frac{2\sqrt{111}}{2}
=\sqrt{111}
$