9v(4v+1)=0

Solution for 9v(4v+1)=0 equation:

9v(4v+1)=0

We multiply parentheses

36v^2+9v=0

a = 36; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·36·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*36}=\frac{-18}{72}
=-1/4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*36}=\frac{0}{72}
=0
$