f^2/2=51

Solution for f^2/2=51 equation:

f^2/2=51

We move all terms to the left:

f^2/2-(51)=0

We multiply all the terms by the denominator


f^2-51*2=0

We add all the numbers together, and all the variables

f^2-102=0

a = 1; b = 0; c = -102;
Δ = b2-4ac
Δ = 02-4·1·(-102)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{102}}{2*1}=\frac{0-2\sqrt{102}}{2}
=-\frac{2\sqrt{102}}{2}
=-\sqrt{102}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{102}}{2*1}=\frac{0+2\sqrt{102}}{2}
=\frac{2\sqrt{102}}{2}
=\sqrt{102}
$