Let x be a positive number such that 2x^2 = 4x + 9. If x can be written in simplified form as $(a + √(b))/(c)$ such that a, b, and c are positive integers, what is a + b + c?

Question

Let x be a positive number such that
`2x^2 = 4x + 9`. If x can be written in simplified form as
`$(a + √(b))/(c)$` such that a, b, and c are positive integers, what is a + b + c?

Answer 1

(4 ± 2
`√(22)`) ÷ 4

Explanation:

i changed equation to be 2x² - 4x - 9 = 0

i used the quadratic formula: (-b ±
`√(b^2-4ac)`) ÷ 2a

where:

a = 2

b = -4

c = -9