Question
$$3x+\frac{15}{4}x^2 = \frac{1}{x^2}-x-\frac{3}{4}x^2$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 3x+\frac{15}{4}x^2 &= \frac{1}{x^2}-x-\frac{3}{4}x^2&& \text{multiply ALL terms by } \color{blue}{ 4x^2 }. \\[1 em]4x^2\cdot3x+4x^2\frac{15}{4}x^2 &= 4x^2\cdot\frac{1}{x^2}-4x^2x-4x^2\frac{3}{4}x^2&& \text{cancel out the denominators} \\[1 em]12x^3+15x^4 &= 4-4x^3-3x^4&& \text{simplify left and right hand side} \\[1 em]15x^4+12x^3 &= -3x^4-4x^3+4&& \text{move all terms to the left hand side } \\[1 em]15x^4+12x^3+3x^4+4x^3-4 &= 0&& \text{simplify left side} \\[1 em]18x^4+16x^3-4 &= 0&& \\[1 em] \end{aligned} $$
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
Equations Solver