2f^2=234

Solution for 2f^2=234 equation:

2f^2=234

We move all terms to the left:

2f^2-(234)=0

a = 2; b = 0; c = -234;
Δ = b2-4ac
Δ = 02-4·2·(-234)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{13}}{2*2}=\frac{0-12\sqrt{13}}{4}
=-\frac{12\sqrt{13}}{4}
=-3\sqrt{13}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{13}}{2*2}=\frac{0+12\sqrt{13}}{4}
=\frac{12\sqrt{13}}{4}
=3\sqrt{13}
$