6v^2-15v-27=0

Solution for 6v^2-15v-27=0 equation:

6v^2-15v-27=0

a = 6; b = -15; c = -27;
Δ = b2-4ac
Δ = -152-4·6·(-27)
Δ = 873
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:

$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{97}}{2*6}=\frac{15-3\sqrt{97}}{12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{97}}{2*6}=\frac{15+3\sqrt{97}}{12}
$