338=v^2/2

Solution for 338=v^2/2 equation:

338=v^2/2

We move all terms to the left:

338-(v^2/2)=0

We get rid of parentheses

-v^2/2+338=0

We multiply all the terms by the denominator


-v^2+338*2=0

We add all the numbers together, and all the variables

-1v^2+676=0

a = -1; b = 0; c = +676;
Δ = b2-4ac
Δ = 02-4·(-1)·676
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-52}{2*-1}=\frac{-52}{-2}
=+26
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+52}{2*-1}=\frac{52}{-2}
=-26
$