Solve -3x^2-24x+5

$$-3 { x }^{ 2 } -24x+5$$

Factor

$$-3\left(x-\left(-\frac{\sqrt{159}}{3}-4\right)\right)\left(x-\left(\frac{\sqrt{159}}{3}-4\right)\right)$$

Steps Using the Quadratic Formula

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.

$$-3x^{2}-24x+5=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\left(-3\right)\times 5}}{2\left(-3\right)}$$

Square -24.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\left(-3\right)\times 5}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{-\left(-24\right)±\sqrt{576+12\times 5}}{2\left(-3\right)}$$

Multiply 12 times 5.

$$x=\frac{-\left(-24\right)±\sqrt{576+60}}{2\left(-3\right)}$$

Add 576 to 60.

$$x=\frac{-\left(-24\right)±\sqrt{636}}{2\left(-3\right)}$$

Take the square root of 636.

$$x=\frac{-\left(-24\right)±2\sqrt{159}}{2\left(-3\right)}$$

The opposite of -24 is 24.

$$x=\frac{24±2\sqrt{159}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{24±2\sqrt{159}}{-6}$$

Now solve the equation x=\frac{24±2\sqrt{159}}{-6} when ± is plus. Add 24 to 2\sqrt{159}.

$$x=\frac{2\sqrt{159}+24}{-6}$$

Divide 24+2\sqrt{159} by -6.

$$x=-\frac{\sqrt{159}}{3}-4$$

Now solve the equation x=\frac{24±2\sqrt{159}}{-6} when ± is minus. Subtract 2\sqrt{159} from 24.

$$x=\frac{24-2\sqrt{159}}{-6}$$

Divide 24-2\sqrt{159} by -6.

$$x=\frac{\sqrt{159}}{3}-4$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -4-\frac{\sqrt{159}}{3} for x_{1} and -4+\frac{\sqrt{159}}{3} for x_{2}.

$$-3x^{2}-24x+5=-3\left(x-\left(-\frac{\sqrt{159}}{3}-4\right)\right)\left(x-\left(\frac{\sqrt{159}}{3}-4\right)\right)$$

Evaluate

$$5-24x-3x^{2}$$