v=5v/2v+8

Solution for v=5v/2v+8 equation:

v=5v/2v+8

We move all terms to the left:

v-(5v/2v+8)=0


Domain of the equation: 2v+8)!=0

v∈R


We get rid of parentheses

v-5v/2v-8=0

We multiply all the terms by the denominator


v*2v-5v-8*2v=0

We add all the numbers together, and all the variables

-5v+v*2v-8*2v=0

Wy multiply elements

2v^2-5v-16v=0

We add all the numbers together, and all the variables

2v^2-21v=0

a = 2; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·2·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*2}=\frac{0}{4}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*2}=\frac{42}{4}
=10+1/2
$