c*c+5=206

Solution for c*c+5=206 equation:

c*c+5=206

We move all terms to the left:

c*c+5-(206)=0

We add all the numbers together, and all the variables

c*c-201=0

Wy multiply elements

c^2-201=0

a = 1; b = 0; c = -201;
Δ = b2-4ac
Δ = 02-4·1·(-201)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{201}}{2*1}=\frac{0-2\sqrt{201}}{2}
=-\frac{2\sqrt{201}}{2}
=-\sqrt{201}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{201}}{2*1}=\frac{0+2\sqrt{201}}{2}
=\frac{2\sqrt{201}}{2}
=\sqrt{201}
$