v^2+6v-27=-9

Solution for v^2+6v-27=-9 equation:

v^2+6v-27=-9

We move all terms to the left:

v^2+6v-27-(-9)=0

We add all the numbers together, and all the variables

v^2+6v-18=0

a = 1; b = 6; c = -18;
Δ = b2-4ac
Δ = 62-4·1·(-18)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*1}=\frac{-6-6\sqrt{3}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*1}=\frac{-6+6\sqrt{3}}{2}
$