5v^2=-9v+5

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

5v^2=-9v+5

We move all terms to the left:

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

We get rid of parentheses

5v^2+9v-5=0

a = 5; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·5·(-5)
Δ = 181
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{-(9)-\sqrt{181}}{2*5}=\frac{-9-\sqrt{181}}{10}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{181}}{2*5}=\frac{-9+\sqrt{181}}{10}
$