Solve 24x^2+25x-6

$$24 { x }^{ 2 } +25x-6$$

Factor

$$24\left(x-\frac{-\sqrt{1201}-25}{48}\right)\left(x-\frac{\sqrt{1201}-25}{48}\right)$$

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.

$$24x^{2}+25x-6=0$$

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.

$$x=\frac{-25±\sqrt{25^{2}-4\times 24\left(-6\right)}}{2\times 24}$$

Square 25.

$$x=\frac{-25±\sqrt{625-4\times 24\left(-6\right)}}{2\times 24}$$

Multiply -4 times 24.

$$x=\frac{-25±\sqrt{625-96\left(-6\right)}}{2\times 24}$$

Multiply -96 times -6.

$$x=\frac{-25±\sqrt{625+576}}{2\times 24}$$

Add 625 to 576.

$$x=\frac{-25±\sqrt{1201}}{2\times 24}$$

Multiply 2 times 24.

$$x=\frac{-25±\sqrt{1201}}{48}$$

Now solve the equation x=\frac{-25±\sqrt{1201}}{48} when ± is plus. Add -25 to \sqrt{1201}.

$$x=\frac{\sqrt{1201}-25}{48}$$

Now solve the equation x=\frac{-25±\sqrt{1201}}{48} when ± is minus. Subtract \sqrt{1201} from -25.

$$x=\frac{-\sqrt{1201}-25}{48}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-25+\sqrt{1201}}{48} for x_{1} and \frac{-25-\sqrt{1201}}{48} for x_{2}.

$$24x^{2}+25x-6=24\left(x-\frac{\sqrt{1201}-25}{48}\right)\left(x-\frac{-\sqrt{1201}-25}{48}\right)$$

Evaluate

$$24x^{2}+25x-6$$