Use the quadratic formula to solve the equation. (Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)
4x^2 - 5x + 7 = 0
Using the quadratic formula, we have:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation 4x^2 - 5x + 7 = 0, we can identify a = 4, b = -5, and c = 7. Plugging these values into the quadratic formula:
x = (-(-5) ± √((-5)^2 - 4(4)(7))) / (2(4))
Simplifying further:
x = (5 ± √(25 - 112)) / 8
x = (5 ± √(-87)) / 8
Since the square root of a negative number results in an imaginary solution, the solutions to this equation are:
x = (5 + √(-87)) / 8 and x = (5 - √(-87)) / 8
These are the exact answers using radicals and i as needed.