5k(k-2)-8k=6

Solution for 5k(k-2)-8k=6 equation:

5k(k-2)-8k=6

We move all terms to the left:

5k(k-2)-8k-(6)=0

We add all the numbers together, and all the variables

-8k+5k(k-2)-6=0

We multiply parentheses

5k^2-8k-10k-6=0

We add all the numbers together, and all the variables

5k^2-18k-6=0

a = 5; b = -18; c = -6;
Δ = b2-4ac
Δ = -182-4·5·(-6)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{111}}{2*5}=\frac{18-2\sqrt{111}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{111}}{2*5}=\frac{18+2\sqrt{111}}{10}
$