Solve 9x^2-28x+44>0

$$9 x ^ { 2 } - 28 x + 44 > 0$$

Solve for x

$$x\in \mathrm{R}$$

Steps Using the Quadratic Formula

To solve the inequality, factor the left hand side. Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$9x^{2}-28x+44=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 9 for a, -28 for b, and 44 for c in the quadratic formula.

$$x=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}-4\times 9\times 44}}{2\times 9}$$

Do the calculations.

$$x=\frac{28±\sqrt{-800}}{18}$$

Since the square root of a negative number is not defined in the real field, there are no solutions. Expression 9x^{2}-28x+44 has the same sign for any x. To determine the sign, calculate the value of the expression for x=0.

$$9\times 0^{2}-28\times 0+44=44$$

The value of the expression 9x^{2}-28x+44 is always positive. Inequality holds for x\in \mathrm{R}.

$$x\in \mathrm{R}$$