Solve 6x^2+25x-15

$$6 { x }^{ 2 } +25x-15$$

Factor

$$6\left(x-\frac{-\sqrt{985}-25}{12}\right)\left(x-\frac{\sqrt{985}-25}{12}\right)$$

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.

$$6x^{2}+25x-15=0$$

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.

$$x=\frac{-25±\sqrt{25^{2}-4\times 6\left(-15\right)}}{2\times 6}$$

Square 25.

$$x=\frac{-25±\sqrt{625-4\times 6\left(-15\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{-25±\sqrt{625-24\left(-15\right)}}{2\times 6}$$

Multiply -24 times -15.

$$x=\frac{-25±\sqrt{625+360}}{2\times 6}$$

Add 625 to 360.

$$x=\frac{-25±\sqrt{985}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{-25±\sqrt{985}}{12}$$

Now solve the equation x=\frac{-25±\sqrt{985}}{12} when ± is plus. Add -25 to \sqrt{985}.

$$x=\frac{\sqrt{985}-25}{12}$$

Now solve the equation x=\frac{-25±\sqrt{985}}{12} when ± is minus. Subtract \sqrt{985} from -25.

$$x=\frac{-\sqrt{985}-25}{12}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-25+\sqrt{985}}{12} for x_{1} and \frac{-25-\sqrt{985}}{12} for x_{2}.

$$6x^{2}+25x-15=6\left(x-\frac{\sqrt{985}-25}{12}\right)\left(x-\frac{-\sqrt{985}-25}{12}\right)$$

Evaluate

$$6x^{2}+25x-15$$