Solve 6x^2+20x-420

$$6 { x }^{ 2 } +20x-420$$

Factor

$$6\left(x-\frac{-\sqrt{655}-5}{3}\right)\left(x-\frac{\sqrt{655}-5}{3}\right)$$

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.

$$6x^{2}+20x-420=0$$

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.

$$x=\frac{-20±\sqrt{20^{2}-4\times 6\left(-420\right)}}{2\times 6}$$

Square 20.

$$x=\frac{-20±\sqrt{400-4\times 6\left(-420\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{-20±\sqrt{400-24\left(-420\right)}}{2\times 6}$$

Multiply -24 times -420.

$$x=\frac{-20±\sqrt{400+10080}}{2\times 6}$$

Add 400 to 10080.

$$x=\frac{-20±\sqrt{10480}}{2\times 6}$$

Take the square root of 10480.

$$x=\frac{-20±4\sqrt{655}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{-20±4\sqrt{655}}{12}$$

Now solve the equation x=\frac{-20±4\sqrt{655}}{12} when ± is plus. Add -20 to 4\sqrt{655}.

$$x=\frac{4\sqrt{655}-20}{12}$$

Divide -20+4\sqrt{655} by 12.

$$x=\frac{\sqrt{655}-5}{3}$$

Now solve the equation x=\frac{-20±4\sqrt{655}}{12} when ± is minus. Subtract 4\sqrt{655} from -20.

$$x=\frac{-4\sqrt{655}-20}{12}$$

Divide -20-4\sqrt{655} by 12.

$$x=\frac{-\sqrt{655}-5}{3}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-5+\sqrt{655}}{3} for x_{1} and \frac{-5-\sqrt{655}}{3} for x_{2}.

$$6x^{2}+20x-420=6\left(x-\frac{\sqrt{655}-5}{3}\right)\left(x-\frac{-\sqrt{655}-5}{3}\right)$$

Evaluate

$$6x^{2}+20x-420$$