k^2-k-27=0

Solution for k^2-k-27=0 equation:

k^2-k-27=0

We add all the numbers together, and all the variables

k^2-1k-27=0

a = 1; b = -1; c = -27;
Δ = b2-4ac
Δ = -12-4·1·(-27)
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{109}}{2*1}=\frac{1-\sqrt{109}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{109}}{2*1}=\frac{1+\sqrt{109}}{2}
$