A quadratic inequality in x is in the standard form of
ax^2+bx+c(>or<)d.
Ex. 3x^2+5x+1>4
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No. This is not an inequality, because you need something > something_else, or less than or 'not equal' or 'greater than or equal', etc. Since it has an x cubed term, it is not a quadratic.
In a linear inequality the variable is only present raised to the first power (which is usually not explicitly shown). In a quadratic the square of the variable is present (or implied). The square can be implied in an inequality such as x + 1/x < 6 (x not 0) This is equivalent to x2 - 6x + 1 < 0
The answer depends on the nature of the inequality: whether it is linear, quadratic or has some other functional form.
Use the quadratic formula for the equality. Then, depending on the coefficient of x2 and the nature of the inequality [>, ≥, ≤, <], determine whether you need the open or closed intervals between the roots or beyond the roots.