Solve 16x^2+9-24xgeq0

$$16 x ^ { 2 } + 9 - 24 x \geq 0$$

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.

$$16x^{2}+9-24x=0$$

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 16 for a, -24 for b, and 9 for c in the quadratic formula.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 16\times 9}}{2\times 16}$$

Do the calculations.

$$x=\frac{24±0}{32}$$

Solutions are the same.

$$x=\frac{3}{4}$$

Rewrite the inequality by using the obtained solutions.

$$16\left(x-\frac{3}{4}\right)^{2}\geq 0$$

Inequality holds for x\in \mathrm{R}.

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