1/3v+2v+v=180

Solution for 1/3v+2v+v=180 equation:

1/3v+2v+v=180

We move all terms to the left:

1/3v+2v+v-(180)=0


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R


We add all the numbers together, and all the variables

3v+1/3v-180=0

We multiply all the terms by the denominator


3v*3v-180*3v+1=0

Wy multiply elements

9v^2-540v+1=0

a = 9; b = -540; c = +1;
Δ = b2-4ac
Δ = -5402-4·9·1
Δ = 291564
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:

$\sqrt{\Delta}=\sqrt{291564}=\sqrt{36*8099}=\sqrt{36}*\sqrt{8099}=6\sqrt{8099}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-6\sqrt{8099}}{2*9}=\frac{540-6\sqrt{8099}}{18}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+6\sqrt{8099}}{2*9}=\frac{540+6\sqrt{8099}}{18}
$