6(5+9k)k=5

Solution for 6(5+9k)k=5 equation:

6(5+9k)k=5

We move all terms to the left:

6(5+9k)k-(5)=0

We add all the numbers together, and all the variables

6(9k+5)k-5=0

We multiply parentheses

54k^2+30k-5=0

a = 54; b = 30; c = -5;
Δ = b2-4ac
Δ = 302-4·54·(-5)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{55}}{2*54}=\frac{-30-6\sqrt{55}}{108}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{55}}{2*54}=\frac{-30+6\sqrt{55}}{108}
$