Using the quadratic formula to solve 4x² - 3x + 9 = 2x + 1, what are the values of x?

Solution:

Given equation 4x² - 3x + 9 = 2x + 1

Arrange the given equation in the standard form ax² + bx+ c= 0

4x² - 3x - 2x + 9 - 1 = 0

4x² - 5x + 8 = 0

Here a= 4, b = -5, c = 8

Apply the quadratic formula,

x = {-b ± √(b² - 4ac)}/2a

= {-(-5) ± √((-5)² - 4(4)(8))}/2(4)

= {5 ± √(25 -128)}/8

= {5 ± √-103}/8

x = {5 ± √103i}/8

Using the quadratic formula to solve 4x² - 3x + 9 = 2x + 1, what are the values of x?

Summary:

Using the quadratic formula to solve 4x² - 3x + 9 = 2x + 1, the values of x are {5 ± √103i}/8.