v=v^2-6v-27

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

v=v^2-6v-27

We move all terms to the left:

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

We get rid of parentheses

-v^2+v+6v+27=0

We add all the numbers together, and all the variables

-1v^2+7v+27=0

a = -1; b = 7; c = +27;
Δ = b2-4ac
Δ = 72-4·(-1)·27
Δ = 157
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{157}}{2*-1}=\frac{-7-\sqrt{157}}{-2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{157}}{2*-1}=\frac{-7+\sqrt{157}}{-2}
$