-1/4v+1/3=-7/2v-1

Solution for -1/4v+1/3=-7/2v-1 equation:

-1/4v+1/3=-7/2v-1

We move all terms to the left:

-1/4v+1/3-(-7/2v-1)=0


Domain of the equation: 4v!=0

v!=0/4

v!=0

v∈R



Domain of the equation: 2v-1)!=0

v∈R


We get rid of parentheses

-1/4v+7/2v+1+1/3=0

We calculate fractions


16v^2/72v^2+(-18v)/72v^2+252v/72v^2+1=0

We multiply all the terms by the denominator


16v^2+(-18v)+252v+1*72v^2=0

We add all the numbers together, and all the variables

16v^2+252v+(-18v)+1*72v^2=0

Wy multiply elements

16v^2+72v^2+252v+(-18v)=0

We get rid of parentheses

16v^2+72v^2+252v-18v=0

We add all the numbers together, and all the variables

88v^2+234v=0

a = 88; b = 234; c = 0;
Δ = b2-4ac
Δ = 2342-4·88·0
Δ = 54756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{54756}=234$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-234}{2*88}=\frac{-468}{176}
=-2+29/44
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+234}{2*88}=\frac{0}{176}
=0
$