5v-3/2v=4

Solution for 5v-3/2v=4 equation:

5v-3/2v=4

We move all terms to the left:

5v-3/2v-(4)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R


We multiply all the terms by the denominator


5v*2v-4*2v-3=0

Wy multiply elements

10v^2-8v-3=0

a = 10; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·10·(-3)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{46}}{2*10}=\frac{8-2\sqrt{46}}{20}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{46}}{2*10}=\frac{8+2\sqrt{46}}{20}
$