-4v+9=9v(v-6)

Solution for -4v+9=9v(v-6) equation:

-4v+9=9v(v-6)

We move all terms to the left:

-4v+9-(9v(v-6))=0


We calculate terms in parentheses: -(9v(v-6)), so:

9v(v-6)

We multiply parentheses

9v^2-54v

Back to the equation:

-(9v^2-54v)


We get rid of parentheses

-9v^2-4v+54v+9=0

We add all the numbers together, and all the variables

-9v^2+50v+9=0

a = -9; b = 50; c = +9;
Δ = b2-4ac
Δ = 502-4·(-9)·9
Δ = 2824
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:

$\sqrt{\Delta}=\sqrt{2824}=\sqrt{4*706}=\sqrt{4}*\sqrt{706}=2\sqrt{706}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{706}}{2*-9}=\frac{-50-2\sqrt{706}}{-18}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{706}}{2*-9}=\frac{-50+2\sqrt{706}}{-18}
$