5v=7/3v-2

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

5v=7/3v-2

We move all terms to the left:

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


Domain of the equation: 3v-2)!=0

v∈R


We get rid of parentheses

5v-7/3v+2=0

We multiply all the terms by the denominator


5v*3v+2*3v-7=0

Wy multiply elements

15v^2+6v-7=0

a = 15; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·15·(-7)
Δ = 456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{114}}{2*15}=\frac{-6-2\sqrt{114}}{30}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{114}}{2*15}=\frac{-6+2\sqrt{114}}{30}
$