Solve the equation

Amanita, let's focus on the equation inside the green rectangle:

Here’s the step-by-step plan to solve this quadratic equation:

Step 1: Identify the type of equation.
This is a quadratic equation because the highest power of $x$ is 2.

Step 2: Recall the quadratic formula.
The quadratic formula for solving $ax^2 + bx + c = 0$ is:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

where $a = 3$, $b = -10$, and $c = 8$.

Step 3: Substitute the values of $a$, $b$, and $c$ into the formula and solve for $x$.

Let’s solve the equation now. Amanita, after solving the equation $3x^2 - 10x + 8 = 0$, we find the solutions:

$x = 2 \quad \text{and} \quad x = \frac{4}{3}$

This means that if you substitute either $x = 2$ or $x = \frac{4}{3}$ back into the original equation, it will make the equation true. These are the values of $x$ that solve the quadratic equation.