Solve 3x+2x^2-6

$$3 x + 2 x ^ { 2 } - 6$$

Factor

$$2\left(x-\frac{-\sqrt{57}-3}{4}\right)\left(x-\frac{\sqrt{57}-3}{4}\right)$$

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.

$$2x^{2}+3x-6=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\times 2\left(-6\right)}}{2\times 2}$$

Square 3.

$$x=\frac{-3±\sqrt{9-4\times 2\left(-6\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-3±\sqrt{9-8\left(-6\right)}}{2\times 2}$$

Multiply -8 times -6.

$$x=\frac{-3±\sqrt{9+48}}{2\times 2}$$

Add 9 to 48.

$$x=\frac{-3±\sqrt{57}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-3±\sqrt{57}}{4}$$

Now solve the equation x=\frac{-3±\sqrt{57}}{4} when ± is plus. Add -3 to \sqrt{57}.

$$x=\frac{\sqrt{57}-3}{4}$$

Now solve the equation x=\frac{-3±\sqrt{57}}{4} when ± is minus. Subtract \sqrt{57} from -3.

$$x=\frac{-\sqrt{57}-3}{4}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{57}}{4} for x_{1} and \frac{-3-\sqrt{57}}{4} for x_{2}.

$$2x^{2}+3x-6=2\left(x-\frac{\sqrt{57}-3}{4}\right)\left(x-\frac{-\sqrt{57}-3}{4}\right)$$

Evaluate

$$2x^{2}+3x-6$$