Final answer:
The given quadratic equation has two real solutions.
Step-by-step explanation:
The given equation is 6x² - 8 = 4x² + 7x. To solve a quadratic equation, we need to make one side of the equation equal to zero. Subtracting 4x² and 7x from both sides, we get 2x² - 7x - 8 = 0.
Now, we can identify the coefficients a, b, and c of the quadratic equation ax² + bx + c = 0. In this case, a = 2, b = -7, and c = -8.
We can use the quadratic formula to find the solutions of the equation. The quadratic formula is: x = (-b ± √(b² - 4ac)) / (2a).
Plugging in the values, we have x = (-(-7) ± √((-7)² - 4(2)(-8))) / (2(2)). Simplifying further, we get x = (7 ± √(49 + 64)) / 4.
Simplifying the square root, we have x = (7 ± √113) / 4. Therefore, the equation has two real solutions.