9k^2=6k+9

Solution for 9k^2=6k+9 equation:

9k^2=6k+9

We move all terms to the left:

9k^2-(6k+9)=0

We get rid of parentheses

9k^2-6k-9=0

a = 9; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·9·(-9)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{10}}{2*9}=\frac{6-6\sqrt{10}}{18}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{10}}{2*9}=\frac{6+6\sqrt{10}}{18}
$