v=4/9v+20

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

v=4/9v+20

We move all terms to the left:

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


Domain of the equation: 9v+20)!=0

v∈R


We get rid of parentheses

v-4/9v-20=0

We multiply all the terms by the denominator


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

Wy multiply elements

9v^2-180v-4=0

a = 9; b = -180; c = -4;
Δ = b2-4ac
Δ = -1802-4·9·(-4)
Δ = 32544
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:

$\sqrt{\Delta}=\sqrt{32544}=\sqrt{144*226}=\sqrt{144}*\sqrt{226}=12\sqrt{226}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-12\sqrt{226}}{2*9}=\frac{180-12\sqrt{226}}{18}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+12\sqrt{226}}{2*9}=\frac{180+12\sqrt{226}}{18}
$