Solve -48x^2+23x+35

$$-48 { x }^{ 2 } +23x+35$$

Factor

$$-48\left(x-\frac{23-\sqrt{7249}}{96}\right)\left(x-\frac{\sqrt{7249}+23}{96}\right)$$

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.

$$-48x^{2}+23x+35=0$$

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.

$$x=\frac{-23±\sqrt{23^{2}-4\left(-48\right)\times 35}}{2\left(-48\right)}$$

Square 23.

$$x=\frac{-23±\sqrt{529-4\left(-48\right)\times 35}}{2\left(-48\right)}$$

Multiply -4 times -48.

$$x=\frac{-23±\sqrt{529+192\times 35}}{2\left(-48\right)}$$

Multiply 192 times 35.

$$x=\frac{-23±\sqrt{529+6720}}{2\left(-48\right)}$$

Add 529 to 6720.

$$x=\frac{-23±\sqrt{7249}}{2\left(-48\right)}$$

Multiply 2 times -48.

$$x=\frac{-23±\sqrt{7249}}{-96}$$

Now solve the equation x=\frac{-23±\sqrt{7249}}{-96} when ± is plus. Add -23 to \sqrt{7249}.

$$x=\frac{\sqrt{7249}-23}{-96}$$

Divide -23+\sqrt{7249} by -96.

$$x=\frac{23-\sqrt{7249}}{96}$$

Now solve the equation x=\frac{-23±\sqrt{7249}}{-96} when ± is minus. Subtract \sqrt{7249} from -23.

$$x=\frac{-\sqrt{7249}-23}{-96}$$

Divide -23-\sqrt{7249} by -96.

$$x=\frac{\sqrt{7249}+23}{96}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{23-\sqrt{7249}}{96} for x_{1} and \frac{23+\sqrt{7249}}{96} for x_{2}.

$$-48x^{2}+23x+35=-48\left(x-\frac{23-\sqrt{7249}}{96}\right)\left(x-\frac{\sqrt{7249}+23}{96}\right)$$

Evaluate

$$35+23x-48x^{2}$$