$$0 = -12000x^4+3000x^3+4000x^2+4000x+6000$$
Answer
$$ \begin{matrix}x_1 = -0.75793 & x_2 = 1.1386 & x_3 = -0.06534+0.75837i \\[1 em] x_4 = -0.06534-0.75837i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 0 &= -12000x^4+3000x^3+4000x^2+4000x+6000&& \text{move all terms to the left hand side } \\[1 em]0+12000x^4-3000x^3-4000x^2-4000x-6000 &= 0&& \text{simplify left side} \\[1 em]12000x^4-3000x^3-4000x^2-4000x-6000 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Polynomial Equations Solver