105=2c^2

Solution for 105=2c^2 equation:

105=2c^2

We move all terms to the left:

105-(2c^2)=0

a = -2; b = 0; c = +105;
Δ = b2-4ac
Δ = 02-4·(-2)·105
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*-2}=\frac{0-2\sqrt{210}}{-4}
=-\frac{2\sqrt{210}}{-4}
=-\frac{\sqrt{210}}{-2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*-2}=\frac{0+2\sqrt{210}}{-4}
=\frac{2\sqrt{210}}{-4}
=\frac{\sqrt{210}}{-2}
$