Solve 5x^2+6x-4

$$5 { x }^{ 2 } +6x-4$$

Factor

$$5\left(x-\frac{-\sqrt{29}-3}{5}\right)\left(x-\frac{\sqrt{29}-3}{5}\right)$$

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.

$$5x^{2}+6x-4=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 5\left(-4\right)}}{2\times 5}$$

Square 6.

$$x=\frac{-6±\sqrt{36-4\times 5\left(-4\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-6±\sqrt{36-20\left(-4\right)}}{2\times 5}$$

Multiply -20 times -4.

$$x=\frac{-6±\sqrt{36+80}}{2\times 5}$$

Add 36 to 80.

$$x=\frac{-6±\sqrt{116}}{2\times 5}$$

Take the square root of 116.

$$x=\frac{-6±2\sqrt{29}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-6±2\sqrt{29}}{10}$$

Now solve the equation x=\frac{-6±2\sqrt{29}}{10} when ± is plus. Add -6 to 2\sqrt{29}.

$$x=\frac{2\sqrt{29}-6}{10}$$

Divide -6+2\sqrt{29} by 10.

$$x=\frac{\sqrt{29}-3}{5}$$

Now solve the equation x=\frac{-6±2\sqrt{29}}{10} when ± is minus. Subtract 2\sqrt{29} from -6.

$$x=\frac{-2\sqrt{29}-6}{10}$$

Divide -6-2\sqrt{29} by 10.

$$x=\frac{-\sqrt{29}-3}{5}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{29}}{5} for x_{1} and \frac{-3-\sqrt{29}}{5} for x_{2}.

$$5x^{2}+6x-4=5\left(x-\frac{\sqrt{29}-3}{5}\right)\left(x-\frac{-\sqrt{29}-3}{5}\right)$$

Evaluate

$$5x^{2}+6x-4$$