9v^2+11v+5=4v^2

Solution for 9v^2+11v+5=4v^2 equation:

9v^2+11v+5=4v^2

We move all terms to the left:

9v^2+11v+5-(4v^2)=0

determiningTheFunctionDomain
9v^2-4v^2+11v+5=0

We add all the numbers together, and all the variables

5v^2+11v+5=0

a = 5; b = 11; c = +5;
Δ = b2-4ac
Δ = 112-4·5·5
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{21}}{2*5}=\frac{-11-\sqrt{21}}{10}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{21}}{2*5}=\frac{-11+\sqrt{21}}{10}
$