Final answer:
To solve the given equation, we'll apply the quadratic formula and find the values of x. However, when checking if these roots satisfy the original equation, we find that none of them do. Therefore, the equation has no solution.
Step-by-step explanation:
To solve the given equation, we'll apply the quadratic formula. The equation is: (2x - 5/2x + 5) + x = 9. First, let's find a common denominator for the fractions in the equation. The equation becomes: ((4x - 5) + 2x(2x + 5))/(2x + 5) = 9. Multiplying through by the denominator, we get: 4x - 5 + 4x^2 + 10x = 9(2x + 5). Simplifying, we have: 4x^2 + 18x - 69 = 0. Using the quadratic formula (x = (-b +/- sqrt(b^2 - 4ac))/(2a)), we can find the values of x. Substituting the values into the formula, we have: x = (-18 +/- sqrt(18^2 - 4(4)(-69)))/(2(4)). Calculating the two roots, we get approximately x = 1.95 and x = -8.45. However, the given equation also includes fractions, so we need to check if any of the roots satisfy the original equation. Substituting x = 1.95 into the original equation, we get approximately 0.18 = 9, which is not true. Substituting x = -8.45, we get approximately -18.45 = 9, which is also not true. Hence, the equation has no solution.