$$\frac{387}{1000}x^3-\frac{144}{1000}x^2+6\cdot\frac{19}{100}x+4\cdot\frac{85}{100} = 5\cdot\frac{67}{1000}$$
Answer
$$ \begin{matrix}x_1 = -1.43221 & x_2 = 0.90215+2.17163i & x_3 = 0.90215-2.17163i \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{387}{1000}x^3-\frac{144}{1000}x^2+6\cdot\frac{19}{100}x+4\cdot\frac{85}{100} &= 5\cdot\frac{67}{1000}&& \text{multiply ALL terms by } \color{blue}{ 1000 }. \\[1 em]1000 \cdot \frac{387}{1000}x^3-1000\frac{144}{1000}x^2+10006\cdot\frac{19}{100}x+1000\cdot4\cdot\frac{85}{100} &= 1000\cdot5\cdot\frac{67}{1000}&& \text{cancel out the denominators} \\[1 em]387x^3-144x^2+1140x+3400 &= 335&& \text{move all terms to the left hand side } \\[1 em]387x^3-144x^2+1140x+3400-335 &= 0&& \text{simplify left side} \\[1 em]387x^3-144x^2+1140x+3065 &= 0&& \\[1 em] \end{aligned} $$
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