5k^2-6k=9

Solution for 5k^2-6k=9 equation:

5k^2-6k=9

We move all terms to the left:

5k^2-6k-(9)=0

a = 5; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·5·(-9)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{6}}{2*5}=\frac{6-6\sqrt{6}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{6}}{2*5}=\frac{6+6\sqrt{6}}{10}
$