39-k2+6k=0

Solution for 39-k2+6k=0 equation:

39-k2+6k=0

We add all the numbers together, and all the variables

-1k^2+6k+39=0

a = -1; b = 6; c = +39;
Δ = b2-4ac
Δ = 62-4·(-1)·39
Δ = 192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8\sqrt{3}}{2*-1}=\frac{-6-8\sqrt{3}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8\sqrt{3}}{2*-1}=\frac{-6+8\sqrt{3}}{-2}
$