Solve -3x^2-8x+4

$$-3 { x }^{ 2 } -8x+4$$

Factor

$$-3\left(x-\frac{-2\sqrt{7}-4}{3}\right)\left(x-\frac{2\sqrt{7}-4}{3}\right)$$

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.

$$-3x^{2}-8x+4=0$$

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.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-3\right)\times 4}}{2\left(-3\right)}$$

Square -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-3\right)\times 4}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{-\left(-8\right)±\sqrt{64+12\times 4}}{2\left(-3\right)}$$

Multiply 12 times 4.

$$x=\frac{-\left(-8\right)±\sqrt{64+48}}{2\left(-3\right)}$$

Add 64 to 48.

$$x=\frac{-\left(-8\right)±\sqrt{112}}{2\left(-3\right)}$$

Take the square root of 112.

$$x=\frac{-\left(-8\right)±4\sqrt{7}}{2\left(-3\right)}$$

The opposite of -8 is 8.

$$x=\frac{8±4\sqrt{7}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{8±4\sqrt{7}}{-6}$$

Now solve the equation x=\frac{8±4\sqrt{7}}{-6} when ± is plus. Add 8 to 4\sqrt{7}.

$$x=\frac{4\sqrt{7}+8}{-6}$$

Divide 8+4\sqrt{7} by -6.

$$x=\frac{-2\sqrt{7}-4}{3}$$

Now solve the equation x=\frac{8±4\sqrt{7}}{-6} when ± is minus. Subtract 4\sqrt{7} from 8.

$$x=\frac{8-4\sqrt{7}}{-6}$$

Divide 8-4\sqrt{7} by -6.

$$x=\frac{2\sqrt{7}-4}{3}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-4-2\sqrt{7}}{3} for x_{1} and \frac{-4+2\sqrt{7}}{3} for x_{2}.

$$-3x^{2}-8x+4=-3\left(x-\frac{-2\sqrt{7}-4}{3}\right)\left(x-\frac{2\sqrt{7}-4}{3}\right)$$

Evaluate

$$4-8x-3x^{2}$$