Solve 8x^2+4x-3

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

Factor

$$8\left(x-\frac{-\sqrt{7}-1}{4}\right)\left(x-\frac{\sqrt{7}-1}{4}\right)$$

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.

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

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.

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

Square 4.

$$x=\frac{-4±\sqrt{16-4\times 8\left(-3\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{-4±\sqrt{16-32\left(-3\right)}}{2\times 8}$$

Multiply -32 times -3.

$$x=\frac{-4±\sqrt{16+96}}{2\times 8}$$

Add 16 to 96.

$$x=\frac{-4±\sqrt{112}}{2\times 8}$$

Take the square root of 112.

$$x=\frac{-4±4\sqrt{7}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{-4±4\sqrt{7}}{16}$$

Now solve the equation x=\frac{-4±4\sqrt{7}}{16} when ± is plus. Add -4 to 4\sqrt{7}.

$$x=\frac{4\sqrt{7}-4}{16}$$

Divide -4+4\sqrt{7} by 16.

$$x=\frac{\sqrt{7}-1}{4}$$

Now solve the equation x=\frac{-4±4\sqrt{7}}{16} when ± is minus. Subtract 4\sqrt{7} from -4.

$$x=\frac{-4\sqrt{7}-4}{16}$$

Divide -4-4\sqrt{7} by 16.

$$x=\frac{-\sqrt{7}-1}{4}$$

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

$$8x^{2}+4x-3=8\left(x-\frac{\sqrt{7}-1}{4}\right)\left(x-\frac{-\sqrt{7}-1}{4}\right)$$

Evaluate

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