Solve 18x^2+7x-6

$$18 { x }^{ 2 } +7x-6$$

Factor

$$18\left(x-\frac{-\sqrt{481}-7}{36}\right)\left(x-\frac{\sqrt{481}-7}{36}\right)$$

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.

$$18x^{2}+7x-6=0$$

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.

$$x=\frac{-7±\sqrt{7^{2}-4\times 18\left(-6\right)}}{2\times 18}$$

Square 7.

$$x=\frac{-7±\sqrt{49-4\times 18\left(-6\right)}}{2\times 18}$$

Multiply -4 times 18.

$$x=\frac{-7±\sqrt{49-72\left(-6\right)}}{2\times 18}$$

Multiply -72 times -6.

$$x=\frac{-7±\sqrt{49+432}}{2\times 18}$$

Add 49 to 432.

$$x=\frac{-7±\sqrt{481}}{2\times 18}$$

Multiply 2 times 18.

$$x=\frac{-7±\sqrt{481}}{36}$$

Now solve the equation x=\frac{-7±\sqrt{481}}{36} when ± is plus. Add -7 to \sqrt{481}.

$$x=\frac{\sqrt{481}-7}{36}$$

Now solve the equation x=\frac{-7±\sqrt{481}}{36} when ± is minus. Subtract \sqrt{481} from -7.

$$x=\frac{-\sqrt{481}-7}{36}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-7+\sqrt{481}}{36} for x_{1} and \frac{-7-\sqrt{481}}{36} for x_{2}.

$$18x^{2}+7x-6=18\left(x-\frac{\sqrt{481}-7}{36}\right)\left(x-\frac{-\sqrt{481}-7}{36}\right)$$

Evaluate

$$18x^{2}+7x-6$$