$$x(x+1)(x+2)\frac{x+3}{24} = 100$$
Answer
$$ \begin{matrix}x_1 = 5.58872 & x_2 = -8.58872 & x_3 = -1.5+6.91014i \\[1 em] x_4 = -1.5-6.91014i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x(x+1)(x+2)\frac{x+3}{24} &= 100&& \text{multiply ALL terms by } \color{blue}{ 24 }. \\[1 em]24x(x+1)(x+2)\frac{x+3}{24} &= 24\cdot100&& \text{cancel out the denominators} \\[1 em]x^4+6x^3+11x^2+6x &= 2400&& \text{move all terms to the left hand side } \\[1 em]x^4+6x^3+11x^2+6x-2400 &= 0&& \\[1 em] \end{aligned} $$
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