I see that you are solving a quadratic equation using the Quadratic Formula. In this case, the equation is 3x² - 4x = 10. Let's go through the steps to find the solutions:
1. Identify the coefficients in the equation:
- In this case, the coefficients are:
- a = 3 (coefficient of x²)
- b = -4 (coefficient of x)
- c = -10 (constant term)
2. Plug the coefficients into the Quadratic Formula:
- The Quadratic Formula is x = (-b ± √(b² - 4ac)) / 2a
3. Substitute the values:
- x = (4 ± √((-4)² - 4 * 3 * (-10))) / 2 * 3
- x = (4 ± √(16 + 120)) / 6
- x = (4 ± √136) / 6
4. Simplify the square root of 136:
- √136 = √(4 * 34) = 2√34
5. Write down the solutions:
- x = (4 ± 2√34) / 6
- x = (2 ± √34) / 3
Therefore, the solutions to the quadratic equation 3x² - 4x = 10 are:
- x = (2 + √34) / 3
- x = (2 - √34) / 3
These are the correct solutions obtained by applying the Quadratic Formula to the given equation.
