-6v(v+9)+3v+6=5v+12

Solution for -6v(v+9)+3v+6=5v+12 equation:

-6v(v+9)+3v+6=5v+12

We move all terms to the left:

-6v(v+9)+3v+6-(5v+12)=0

We add all the numbers together, and all the variables

3v-6v(v+9)-(5v+12)+6=0

We multiply parentheses

-6v^2+3v-54v-(5v+12)+6=0

We get rid of parentheses

-6v^2+3v-54v-5v-12+6=0

We add all the numbers together, and all the variables

-6v^2-56v-6=0

a = -6; b = -56; c = -6;
Δ = b2-4ac
Δ = -562-4·(-6)·(-6)
Δ = 2992
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:

$\sqrt{\Delta}=\sqrt{2992}=\sqrt{16*187}=\sqrt{16}*\sqrt{187}=4\sqrt{187}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{187}}{2*-6}=\frac{56-4\sqrt{187}}{-12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{187}}{2*-6}=\frac{56+4\sqrt{187}}{-12}
$