576/2v+2v=68

Solution for 576/2v+2v=68 equation:

576/2v+2v=68

We move all terms to the left:

576/2v+2v-(68)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R


We add all the numbers together, and all the variables

2v+576/2v-68=0

We multiply all the terms by the denominator


2v*2v-68*2v+576=0

Wy multiply elements

4v^2-136v+576=0

a = 4; b = -136; c = +576;
Δ = b2-4ac
Δ = -1362-4·4·576
Δ = 9280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9280}=\sqrt{64*145}=\sqrt{64}*\sqrt{145}=8\sqrt{145}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-8\sqrt{145}}{2*4}=\frac{136-8\sqrt{145}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+8\sqrt{145}}{2*4}=\frac{136+8\sqrt{145}}{8}
$