3/2v-5/7v=1

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

3/2v-5/7v=1

We move all terms to the left:

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


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 7v!=0

v!=0/7

v!=0

v∈R


We calculate fractions


21v/14v^2+(-10v)/14v^2-1=0

We multiply all the terms by the denominator


21v+(-10v)-1*14v^2=0

Wy multiply elements

-14v^2+21v+(-10v)=0

We get rid of parentheses

-14v^2+21v-10v=0

We add all the numbers together, and all the variables

-14v^2+11v=0

a = -14; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-14)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-14}=\frac{-22}{-28}
=11/14
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-14}=\frac{0}{-28}
=0
$