1/14-5/2v=4/7v

Solution for 1/14-5/2v=4/7v equation:

1/14-5/2v=4/7v

We move all terms to the left:

1/14-5/2v-(4/7v)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 7v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

-5/2v-(+4/7v)+1/14=0

We get rid of parentheses

-5/2v-4/7v+1/14=0

We calculate fractions


98v^2/196v^2+(-490v)/196v^2+(-112v)/196v^2=0

We multiply all the terms by the denominator


98v^2+(-490v)+(-112v)=0

We get rid of parentheses

98v^2-490v-112v=0

We add all the numbers together, and all the variables

98v^2-602v=0

a = 98; b = -602; c = 0;
Δ = b2-4ac
Δ = -6022-4·98·0
Δ = 362404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{362404}=602$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-602)-602}{2*98}=\frac{0}{196}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-602)+602}{2*98}=\frac{1204}{196}
=6+1/7
$