Solve 3x^2+19x-60

$$3 { x }^{ 2 } +19x-60$$

Factor

$$3\left(x-\frac{-\sqrt{1081}-19}{6}\right)\left(x-\frac{\sqrt{1081}-19}{6}\right)$$

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.

$$3x^{2}+19x-60=0$$

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.

$$x=\frac{-19±\sqrt{19^{2}-4\times 3\left(-60\right)}}{2\times 3}$$

Square 19.

$$x=\frac{-19±\sqrt{361-4\times 3\left(-60\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{-19±\sqrt{361-12\left(-60\right)}}{2\times 3}$$

Multiply -12 times -60.

$$x=\frac{-19±\sqrt{361+720}}{2\times 3}$$

Add 361 to 720.

$$x=\frac{-19±\sqrt{1081}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-19±\sqrt{1081}}{6}$$

Now solve the equation x=\frac{-19±\sqrt{1081}}{6} when ± is plus. Add -19 to \sqrt{1081}.

$$x=\frac{\sqrt{1081}-19}{6}$$

Now solve the equation x=\frac{-19±\sqrt{1081}}{6} when ± is minus. Subtract \sqrt{1081} from -19.

$$x=\frac{-\sqrt{1081}-19}{6}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-19+\sqrt{1081}}{6} for x_{1} and \frac{-19-\sqrt{1081}}{6} for x_{2}.

$$3x^{2}+19x-60=3\left(x-\frac{\sqrt{1081}-19}{6}\right)\left(x-\frac{-\sqrt{1081}-19}{6}\right)$$

Evaluate

$$3x^{2}+19x-60$$