9v^2-5=9v

Solution for 9v^2-5=9v equation:

9v^2-5=9v

We move all terms to the left:

9v^2-5-(9v)=0

a = 9; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·9·(-5)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{29}}{2*9}=\frac{9-3\sqrt{29}}{18}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{29}}{2*9}=\frac{9+3\sqrt{29}}{18}
$