3(6-k)k=3

Solution for 3(6-k)k=3 equation:

3(6-k)k=3

We move all terms to the left:

3(6-k)k-(3)=0

We add all the numbers together, and all the variables

3(-1k+6)k-3=0

We multiply parentheses

-3k^2+18k-3=0

a = -3; b = 18; c = -3;
Δ = b2-4ac
Δ = 182-4·(-3)·(-3)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12\sqrt{2}}{2*-3}=\frac{-18-12\sqrt{2}}{-6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12\sqrt{2}}{2*-3}=\frac{-18+12\sqrt{2}}{-6}
$