45+88=c^2

Solution for 45+88=c^2 equation:

45+88=c^2

We move all terms to the left:

45+88-(c^2)=0

We add all the numbers together, and all the variables

-1c^2+133=0

a = -1; b = 0; c = +133;
Δ = b2-4ac
Δ = 02-4·(-1)·133
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{133}}{2*-1}=\frac{0-2\sqrt{133}}{-2}
=-\frac{2\sqrt{133}}{-2}
=-\frac{\sqrt{133}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{133}}{2*-1}=\frac{0+2\sqrt{133}}{-2}
=\frac{2\sqrt{133}}{-2}
=\frac{\sqrt{133}}{-1}
$