18-3k(-k+6)=15

Solution for 18-3k(-k+6)=15 equation:

18-3k(-k+6)=15

We move all terms to the left:

18-3k(-k+6)-(15)=0

We add all the numbers together, and all the variables

-3k(-1k+6)+18-15=0

We add all the numbers together, and all the variables

-3k(-1k+6)+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}
$