$$\frac{2}{3}x^2+15x^2 = 684$$
Answer
$$ \begin{matrix}x_1 = -6 \dfrac{\sqrt{ 2679 }}{ 47 } & x_2 = \dfrac{ 6 \sqrt{ 2679}}{ 47 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2}{3}x^2+15x^2 &= 684&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{2}{3}x^2+3\cdot15x^2 &= 3\cdot684&& \text{cancel out the denominators} \\[1 em]2x^2+45x^2 &= 2052&& \text{simplify left side} \\[1 em]47x^2 &= 2052&& \text{move all terms to the left hand side } \\[1 em]47x^2-2052 &= 0&& \\[1 em] \end{aligned} $$
$ 47x^{2}-2052 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
This page was created using
Polynomial Equations Solver