Solve 3x^2+14x-15

$$3 { x }^{ 2 } +14x-15$$

Factor

$$3\left(x-\frac{-\sqrt{94}-7}{3}\right)\left(x-\frac{\sqrt{94}-7}{3}\right)$$

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.

$$3x^{2}+14x-15=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}-4\times 3\left(-15\right)}}{2\times 3}$$

Square 14.

$$x=\frac{-14±\sqrt{196-4\times 3\left(-15\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{-14±\sqrt{196-12\left(-15\right)}}{2\times 3}$$

Multiply -12 times -15.

$$x=\frac{-14±\sqrt{196+180}}{2\times 3}$$

Add 196 to 180.

$$x=\frac{-14±\sqrt{376}}{2\times 3}$$

Take the square root of 376.

$$x=\frac{-14±2\sqrt{94}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-14±2\sqrt{94}}{6}$$

Now solve the equation x=\frac{-14±2\sqrt{94}}{6} when ± is plus. Add -14 to 2\sqrt{94}.

$$x=\frac{2\sqrt{94}-14}{6}$$

Divide -14+2\sqrt{94} by 6.

$$x=\frac{\sqrt{94}-7}{3}$$

Now solve the equation x=\frac{-14±2\sqrt{94}}{6} when ± is minus. Subtract 2\sqrt{94} from -14.

$$x=\frac{-2\sqrt{94}-14}{6}$$

Divide -14-2\sqrt{94} by 6.

$$x=\frac{-\sqrt{94}-7}{3}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-7+\sqrt{94}}{3} for x_{1} and \frac{-7-\sqrt{94}}{3} for x_{2}.

$$3x^{2}+14x-15=3\left(x-\frac{\sqrt{94}-7}{3}\right)\left(x-\frac{-\sqrt{94}-7}{3}\right)$$

Evaluate

$$3x^{2}+14x-15$$