$$1500x^4+7500x^3+15000x^2+15500x+8500 = 7088$$
Answer
$$ \begin{matrix}x_1 = -0.10037 & x_2 = -2.6457 & x_3 = -1.12697+1.5083i \\[1 em] x_4 = -1.12697-1.5083i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 1500x^4+7500x^3+15000x^2+15500x+8500 &= 7088&& \text{move all terms to the left hand side } \\[1 em]1500x^4+7500x^3+15000x^2+15500x+8500-7088 &= 0&& \text{simplify left side} \\[1 em]1500x^4+7500x^3+15000x^2+15500x+1412 &= 0&& \\[1 em] \end{aligned} $$
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