3(v^2+9v+15)=0

Solution for 3(v^2+9v+15)=0 equation:

3(v^2+9v+15)=0

We multiply parentheses

3v^2+27v+45=0

a = 3; b = 27; c = +45;
Δ = b2-4ac
Δ = 272-4·3·45
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{21}}{2*3}=\frac{-27-3\sqrt{21}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{21}}{2*3}=\frac{-27+3\sqrt{21}}{6}
$