$$8k^2-20k+\frac{12}{k-2} = 0$$
Answer
$$ \begin{matrix}k_1 = -0.24367 & k_2 = 2.37183+0.72821i & k_3 = 2.37183-0.72821i \end{matrix} $$
Explanation
$$ \begin{aligned} 8k^2-20k+\frac{12}{k-2} &= 0&& \text{multiply ALL terms by } \color{blue}{ k-2 }. \\[1 em](k-2)\cdot8k^2-(k-2)\cdot20k+(k-2)\cdot\frac{12}{k-2} &= (k-2)\cdot0&& \text{cancel out the denominators} \\[1 em]8k^3-16k^2-(20k^2-40k)+12 &= 0&& \text{simplify left side} \\[1 em]8k^3-16k^2-20k^2+40k+12 &= 0&& \\[1 em]8k^3-36k^2+40k+12 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Polynomial Equations Solver