Solve n/4/2left(2*10+left(n/4-1right)20right)=9000

$$\frac{ \frac{ n }{ 4 } }{ 2 } \left( 2 \cdot 10+ \left( \frac{ n }{ 4 } -1 \right) 20 \right) = 9000$$

Solve for n

$$n=120$$

$$n=-120$$

Steps by Finding Square Root

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\times \frac{n}{4}\left(2\times 10+\left(\frac{n}{4}-1\right)\times 20\right)=36000$$

Multiply 2 and 10 to get 20.

$$2\times \frac{n}{4}\left(20+\left(\frac{n}{4}-1\right)\times 20\right)=36000$$

Use the distributive property to multiply \frac{n}{4}-1 by 20.

$$2\times \frac{n}{4}\left(20+20\times \frac{n}{4}-20\right)=36000$$

Cancel out 4, the greatest common factor in 20 and 4.

$$2\times \frac{n}{4}\left(20+5n-20\right)=36000$$

Subtract 20 from 20 to get 0.

$$2\times \frac{n}{4}\times 5n=36000$$

Multiply 2 and 5 to get 10.

$$10\times \frac{n}{4}n=36000$$

Express 10\times \frac{n}{4} as a single fraction.

$$\frac{10n}{4}n=36000$$

Express \frac{10n}{4}n as a single fraction.

$$\frac{10nn}{4}=36000$$

Multiply n and n to get n^{2}.

$$\frac{10n^{2}}{4}=36000$$

Divide 10n^{2} by 4 to get \frac{5}{2}n^{2}.

$$\frac{5}{2}n^{2}=36000$$

Multiply both sides by \frac{2}{5}, the reciprocal of \frac{5}{2}.

$$n^{2}=36000\times \frac{2}{5}$$

Express 36000\times \frac{2}{5} as a single fraction.

$$n^{2}=\frac{36000\times 2}{5}$$

Multiply 36000 and 2 to get 72000.

$$n^{2}=\frac{72000}{5}$$

Divide 72000 by 5 to get 14400.

$$n^{2}=14400$$

Take the square root of both sides of the equation.

$$n=120 n=-120$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\times \frac{n}{4}\left(2\times 10+\left(\frac{n}{4}-1\right)\times 20\right)=36000$$

Multiply 2 and 10 to get 20.

$$2\times \frac{n}{4}\left(20+\left(\frac{n}{4}-1\right)\times 20\right)=36000$$

Use the distributive property to multiply \frac{n}{4}-1 by 20.

$$2\times \frac{n}{4}\left(20+20\times \frac{n}{4}-20\right)=36000$$

Cancel out 4, the greatest common factor in 20 and 4.

$$2\times \frac{n}{4}\left(20+5n-20\right)=36000$$

Subtract 20 from 20 to get 0.

$$2\times \frac{n}{4}\times 5n=36000$$

Multiply 2 and 5 to get 10.

$$10\times \frac{n}{4}n=36000$$

Express 10\times \frac{n}{4} as a single fraction.

$$\frac{10n}{4}n=36000$$

Express \frac{10n}{4}n as a single fraction.

$$\frac{10nn}{4}=36000$$

Multiply n and n to get n^{2}.

$$\frac{10n^{2}}{4}=36000$$

Divide 10n^{2} by 4 to get \frac{5}{2}n^{2}.

$$\frac{5}{2}n^{2}=36000$$

Subtract 36000 from both sides.

$$\frac{5}{2}n^{2}-36000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{5}{2} for a, 0 for b, and -36000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times \frac{5}{2}\left(-36000\right)}}{2\times \frac{5}{2}}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times \frac{5}{2}\left(-36000\right)}}{2\times \frac{5}{2}}$$

Multiply -4 times \frac{5}{2}.

$$n=\frac{0±\sqrt{-10\left(-36000\right)}}{2\times \frac{5}{2}}$$

Multiply -10 times -36000.

$$n=\frac{0±\sqrt{360000}}{2\times \frac{5}{2}}$$

Take the square root of 360000.

$$n=\frac{0±600}{2\times \frac{5}{2}}$$

Multiply 2 times \frac{5}{2}.

$$n=\frac{0±600}{5}$$

Now solve the equation n=\frac{0±600}{5} when ± is plus. Divide 600 by 5.

$$n=120$$

Now solve the equation n=\frac{0±600}{5} when ± is minus. Divide -600 by 5.

$$n=-120$$

The equation is now solved.

$$n=120 n=-120$$