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

We add all the numbers together, and all the variables

31v-1*14v^2=0

Wy multiply elements

-14v^2+31v=0

a = -14; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-14)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-14}=\frac{-62}{-28}
=2+3/14
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-14}=\frac{0}{-28}
=0
$