2/3v+5/7v=1

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

2/3v+5/7v=1

We move all terms to the left:

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


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: 7v!=0

v!=0/7

v!=0

v∈R


We calculate fractions


14v/21v^2+15v/21v^2-1=0

We multiply all the terms by the denominator


14v+15v-1*21v^2=0

We add all the numbers together, and all the variables

29v-1*21v^2=0

Wy multiply elements

-21v^2+29v=0

a = -21; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-21)·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*-21}=\frac{-58}{-42}
=1+8/21
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-21}=\frac{0}{-42}
=0
$