Solve 80=piD^2/4

$$80 = \frac { \pi D ^ { 2 } } { 4 }$$

Solve for D

$$D=8\sqrt{\frac{5}{\pi }}\approx 10.092530088$$

$$D=-8\sqrt{\frac{5}{\pi }}\approx -10.092530088$$

Steps by Finding Square Root

Multiply both sides by 4.

$$80\times 4=\pi D^{2}$$

Multiply 80 and 4 to get 320.

$$320=\pi D^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\pi D^{2}=320$$

Divide both sides by \pi .

$$\frac{\pi D^{2}}{\pi }=\frac{320}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$D^{2}=\frac{320}{\pi }$$

Take the square root of both sides of the equation.

$$D=\frac{40}{\sqrt{5\pi }} D=-\frac{40}{\sqrt{5\pi }}$$

Steps Using the Quadratic Formula

Multiply both sides by 4.

$$80\times 4=\pi D^{2}$$

Multiply 80 and 4 to get 320.

$$320=\pi D^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\pi D^{2}=320$$

Subtract 320 from both sides.

$$\pi D^{2}-320=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -320 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$D=\frac{0±\sqrt{0^{2}-4\pi \left(-320\right)}}{2\pi }$$

Square 0.

$$D=\frac{0±\sqrt{-4\pi \left(-320\right)}}{2\pi }$$

Multiply -4 times \pi .

$$D=\frac{0±\sqrt{\left(-4\pi \right)\left(-320\right)}}{2\pi }$$

Multiply -4\pi times -320.

$$D=\frac{0±\sqrt{1280\pi }}{2\pi }$$

Take the square root of 1280\pi .

$$D=\frac{0±16\sqrt{5\pi }}{2\pi }$$

Now solve the equation D=\frac{0±16\sqrt{5\pi }}{2\pi } when ± is plus.

$$D=\frac{40}{\sqrt{5\pi }}$$

Now solve the equation D=\frac{0±16\sqrt{5\pi }}{2\pi } when ± is minus.

$$D=-\frac{40}{\sqrt{5\pi }}$$

The equation is now solved.

$$D=\frac{40}{\sqrt{5\pi }} D=-\frac{40}{\sqrt{5\pi }}$$