c2=674

Solution for c2=674 equation:

c2=674

We move all terms to the left:

c2-(674)=0

We add all the numbers together, and all the variables

c^2-674=0

a = 1; b = 0; c = -674;
Δ = b2-4ac
Δ = 02-4·1·(-674)
Δ = 2696
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:

$\sqrt{\Delta}=\sqrt{2696}=\sqrt{4*674}=\sqrt{4}*\sqrt{674}=2\sqrt{674}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{674}}{2*1}=\frac{0-2\sqrt{674}}{2}
=-\frac{2\sqrt{674}}{2}
=-\sqrt{674}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{674}}{2*1}=\frac{0+2\sqrt{674}}{2}
=\frac{2\sqrt{674}}{2}
=\sqrt{674}
$