# Solve the inequalty 3x^2 - 9x + 5 < 0

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### 2 Answers

You need to attach the equation such that:

`3x^2 - 9x + 5 = 0 => 3x^2 - 9x = -5 => x^2 - 3x = -5/3`

You need to complete the square, such that:

`x^2 - 3x + 9/4 = -5/3 + 9/4`

`(x - 3/2)^2 = (-20+27)/12 => x - 3/2 = +-sqrt(7/12)`

`x = 3/2 +- sqrt21/6`

**You should notice that the quadratic is negative if **`3/2 - sqrt21/6 < x < 3/2 + sqrt21/6.`

One way to solve the inequality is to draw a graph of the function

f(x) = 3x^2-9x+5

The area between the roots is the area where the graph goes below the x axis. This area represents the solution of the inequality.

First, we'll determine the roots of the function:

3x^2-9x+5 = 0

We'll apply the quadratic formula:

x1 = [9+sqrt(81 - 60)]/6

x1 = (9+sqrt21)/6

x2 = (9-sqrt21)/6

The expresison is negative when x is located in the interval

((9-sqrt21)/6 ; (9+sqrt21)/6)