Solve 6x^2+11x-9

$$6 { x }^{ 2 } +11x-9$$

Factor

$$6\left(x-\frac{-\sqrt{337}-11}{12}\right)\left(x-\frac{\sqrt{337}-11}{12}\right)$$

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.

$$6x^{2}+11x-9=0$$

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.

$$x=\frac{-11±\sqrt{11^{2}-4\times 6\left(-9\right)}}{2\times 6}$$

Square 11.

$$x=\frac{-11±\sqrt{121-4\times 6\left(-9\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{-11±\sqrt{121-24\left(-9\right)}}{2\times 6}$$

Multiply -24 times -9.

$$x=\frac{-11±\sqrt{121+216}}{2\times 6}$$

Add 121 to 216.

$$x=\frac{-11±\sqrt{337}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{-11±\sqrt{337}}{12}$$

Now solve the equation x=\frac{-11±\sqrt{337}}{12} when ± is plus. Add -11 to \sqrt{337}.

$$x=\frac{\sqrt{337}-11}{12}$$

Now solve the equation x=\frac{-11±\sqrt{337}}{12} when ± is minus. Subtract \sqrt{337} from -11.

$$x=\frac{-\sqrt{337}-11}{12}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-11+\sqrt{337}}{12} for x_{1} and \frac{-11-\sqrt{337}}{12} for x_{2}.

$$6x^{2}+11x-9=6\left(x-\frac{\sqrt{337}-11}{12}\right)\left(x-\frac{-\sqrt{337}-11}{12}\right)$$

Evaluate

$$6x^{2}+11x-9$$