2/5v-7/3v=1

Solution for 2/5v-7/3v=1 equation:

2/5v-7/3v=1

We move all terms to the left:

2/5v-7/3v-(1)=0


Domain of the equation: 5v!=0

v!=0/5

v!=0

v∈R



Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R


We calculate fractions


6v/15v^2+(-35v)/15v^2-1=0

We multiply all the terms by the denominator


6v+(-35v)-1*15v^2=0

Wy multiply elements

-15v^2+6v+(-35v)=0

We get rid of parentheses

-15v^2+6v-35v=0

We add all the numbers together, and all the variables

-15v^2-29v=0

a = -15; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·(-15)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*-15}=\frac{0}{-30}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*-15}=\frac{58}{-30}
=-1+14/15
$