Solve the Quadratic Equation: x²/3 + x - 10/3 = 0 Step-by-Step

To solve the equation $\frac{x^2}{3} + x - \frac{10}{3} = 0$, we will take these steps:

• Step 1: Clear the fractions by multiplying the entire equation by 3:
  $3 \times \frac{x^2}{3} + 3 \times x - 3 \times \frac{10}{3} = 0$.
• Step 2: Simplify to get:
  $x^2 + 3x - 10 = 0$.
• Step 3: Identify coefficients for the quadratic formula where $a = 1$, $b = 3$, and $c = -10$.
• Step 4: Apply the quadratic formula:
  $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-3 \pm \sqrt{3^2 - 4 \times 1 \times (-10)}}{2 \times 1}$.
• Step 5: Compute under the square root:
  $3^2 - 4 \times 1 \times (-10) = 9 + 40 = 49$.
• Step 6: Calculate the square root of 49, which is 7.
• Step 7: Substitute back to find the values of x:
  $x = \frac{-3 \pm 7}{2}$.
• Step 8: Calculate the two possible solutions:
  For $x_1$: $x = \frac{-3 + 7}{2} = 2$.
  For $x_2$: $x = \frac{-3 - 7}{2} = -5$.

Therefore, the solutions to the equation are $x_1 = 2$ and $x_2 = -5$.

Thus, the answer is: $x_1=2, x_2=-5$.