2k^2=-27k-81

Solution for 2k^2=-27k-81 equation:

2k^2=-27k-81

We move all terms to the left:

2k^2-(-27k-81)=0

We get rid of parentheses

2k^2+27k+81=0

a = 2; b = 27; c = +81;
Δ = b2-4ac
Δ = 272-4·2·81
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-9}{2*2}=\frac{-36}{4}
=-9
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+9}{2*2}=\frac{-18}{4}
=-4+1/2
$