-1/3v-1/4=1/4v-6

Solution for -1/3v-1/4=1/4v-6 equation:

-1/3v-1/4=1/4v-6

We move all terms to the left:

-1/3v-1/4-(1/4v-6)=0


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: 4v-6)!=0

v∈R


We get rid of parentheses

-1/3v-1/4v+6-1/4=0

We calculate fractions


(-64v)/192v^2+(-3v)/192v^2+(-3v)/192v^2+6=0

We multiply all the terms by the denominator


(-64v)+(-3v)+(-3v)+6*192v^2=0

Wy multiply elements

1152v^2+(-64v)+(-3v)+(-3v)=0

We get rid of parentheses

1152v^2-64v-3v-3v=0

We add all the numbers together, and all the variables

1152v^2-70v=0

a = 1152; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·1152·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*1152}=\frac{0}{2304}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*1152}=\frac{140}{2304}
=35/576
$