c2=149

Solution for c2=149 equation:

c2=149

We move all terms to the left:

c2-(149)=0

We add all the numbers together, and all the variables

c^2-149=0

a = 1; b = 0; c = -149;
Δ = b2-4ac
Δ = 02-4·1·(-149)
Δ = 596
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:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{149}}{2*1}=\frac{0-2\sqrt{149}}{2}
=-\frac{2\sqrt{149}}{2}
=-\sqrt{149}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{149}}{2*1}=\frac{0+2\sqrt{149}}{2}
=\frac{2\sqrt{149}}{2}
=\sqrt{149}
$