v=9/4v+20

Solution for v=9/4v+20 equation:

v=9/4v+20

We move all terms to the left:

v-(9/4v+20)=0


Domain of the equation: 4v+20)!=0

v∈R


We get rid of parentheses

v-9/4v-20=0

We multiply all the terms by the denominator


v*4v-20*4v-9=0

Wy multiply elements

4v^2-80v-9=0

a = 4; b = -80; c = -9;
Δ = b2-4ac
Δ = -802-4·4·(-9)
Δ = 6544
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:

$\sqrt{\Delta}=\sqrt{6544}=\sqrt{16*409}=\sqrt{16}*\sqrt{409}=4\sqrt{409}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{409}}{2*4}=\frac{80-4\sqrt{409}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{409}}{2*4}=\frac{80+4\sqrt{409}}{8}
$