Solve 2n-3/4+2-5sqrt{3}=1/2pi

$$2 n - \frac { 3 } { 4 } + 2 - 5 \sqrt { 3 } = \frac { 1 } { 2 } \pi$$

Solve for n

$$n=\frac{\pi }{4}+\frac{5\sqrt{3}}{2}-\frac{5}{8}\approx 4.490525182$$

Steps for Solving Linear Equation

Convert 2 to fraction \frac{8}{4}.

$$2n-\frac{3}{4}+\frac{8}{4}-5\sqrt{3}=\frac{1}{2}\pi$$

Since -\frac{3}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$2n+\frac{-3+8}{4}-5\sqrt{3}=\frac{1}{2}\pi$$

Add -3 and 8 to get 5.

$$2n+\frac{5}{4}-5\sqrt{3}=\frac{1}{2}\pi$$

Subtract \frac{5}{4} from both sides.

$$2n-5\sqrt{3}=\frac{1}{2}\pi -\frac{5}{4}$$

Add 5\sqrt{3} to both sides.

$$2n=\frac{1}{2}\pi -\frac{5}{4}+5\sqrt{3}$$

The equation is in standard form.

$$2n=\frac{\pi }{2}+5\sqrt{3}-\frac{5}{4}$$

Divide both sides by 2.

$$\frac{2n}{2}=\frac{\frac{\pi }{2}+5\sqrt{3}-\frac{5}{4}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$n=\frac{\frac{\pi }{2}+5\sqrt{3}-\frac{5}{4}}{2}$$

Divide \frac{\pi }{2}-\frac{5}{4}+5\sqrt{3} by 2.

$$n=\frac{\pi }{4}+\frac{5\sqrt{3}}{2}-\frac{5}{8}$$