Solve n*frac{2pmsqrt{(-2)^2-4(1)(-120)}}{2(1)}

$$n \cdot \frac { 2 \pm \sqrt { ( - 2 ) ^ { 2 } - 4 ( 1 ) ( - 120 ) } } { 2 ( 1 ) }$$

Evaluate

$$\frac{n\left(2±22\right)}{2}$$

Solution Steps

Calculate -2 to the power of 2 and get 4.

$$n\times \frac{2±\sqrt{4-4\times 1\left(-120\right)}}{2\times 1}$$

Multiply 4 and 1 to get 4.

$$n\times \frac{2±\sqrt{4-4\left(-120\right)}}{2\times 1}$$

Multiply 4 and -120 to get -480.

$$n\times \frac{2±\sqrt{4-\left(-480\right)}}{2\times 1}$$

The opposite of -480 is 480.

$$n\times \frac{2±\sqrt{4+480}}{2\times 1}$$

Add 4 and 480 to get 484.

$$n\times \frac{2±\sqrt{484}}{2\times 1}$$

Calculate the square root of 484 and get 22.

$$n\times \frac{2±22}{2\times 1}$$

Multiply 2 and 1 to get 2.

$$n\times \frac{2±22}{2}$$

Express n\times \frac{2±22}{2} as a single fraction.

$$\frac{n\left(2±22\right)}{2}$$

Differentiate w.r.t. n

$$\frac{2±22}{2}$$