5/6v+2=7/10v

Solution for 5/6v+2=7/10v equation:

5/6v+2=7/10v

We move all terms to the left:

5/6v+2-(7/10v)=0


Domain of the equation: 6v!=0

v!=0/6

v!=0

v∈R



Domain of the equation: 10v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

5/6v-(+7/10v)+2=0

We get rid of parentheses

5/6v-7/10v+2=0

We calculate fractions


50v/60v^2+(-42v)/60v^2+2=0

We multiply all the terms by the denominator


50v+(-42v)+2*60v^2=0

Wy multiply elements

120v^2+50v+(-42v)=0

We get rid of parentheses

120v^2+50v-42v=0

We add all the numbers together, and all the variables

120v^2+8v=0

a = 120; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·120·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*120}=\frac{-16}{240}
=-1/15
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*120}=\frac{0}{240}
=0
$