334=f^2

Solution for 334=f^2 equation:

334=f^2

We move all terms to the left:

334-(f^2)=0

We add all the numbers together, and all the variables

-1f^2+334=0

a = -1; b = 0; c = +334;
Δ = b2-4ac
Δ = 02-4·(-1)·334
Δ = 1336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1336}=\sqrt{4*334}=\sqrt{4}*\sqrt{334}=2\sqrt{334}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{334}}{2*-1}=\frac{0-2\sqrt{334}}{-2}
=-\frac{2\sqrt{334}}{-2}
=-\frac{\sqrt{334}}{-1}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{334}}{2*-1}=\frac{0+2\sqrt{334}}{-2}
=\frac{2\sqrt{334}}{-2}
=\frac{\sqrt{334}}{-1}
$