Solve 2pi/x*8.6*10^-6*sqrt{1.4672^2-1.4621^2}=2.405

$$\frac { 2 \pi } { x } \times 8.6 \times 10 ^ { - 6 } \times \sqrt { 1.4672 ^ { 2 } - 1.4621 ^ { 2 } } = 2.405$$

Solve for x

$$x=\frac{43\pi \sqrt{1493943}}{60125000000}\approx 0.000002746$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$8.6\times 2\pi \times 10^{-6}\sqrt{1.4672^{2}-1.4621^{2}}=2.405x$$

Multiply 8.6 and 2 to get 17.2.

$$17.2\pi \times 10^{-6}\sqrt{1.4672^{2}-1.4621^{2}}=2.405x$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$17.2\pi \times \frac{1}{1000000}\sqrt{1.4672^{2}-1.4621^{2}}=2.405x$$

Multiply 17.2 and \frac{1}{1000000} to get \frac{43}{2500000}.

$$\frac{43}{2500000}\pi \sqrt{1.4672^{2}-1.4621^{2}}=2.405x$$

Calculate 1.4672 to the power of 2 and get 2.15267584.

$$\frac{43}{2500000}\pi \sqrt{2.15267584-1.4621^{2}}=2.405x$$

Calculate 1.4621 to the power of 2 and get 2.13773641.

$$\frac{43}{2500000}\pi \sqrt{2.15267584-2.13773641}=2.405x$$

Subtract 2.13773641 from 2.15267584 to get 0.01493943.

$$\frac{43}{2500000}\pi \sqrt{0.01493943}=2.405x$$

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

$$2.405x=\frac{43}{2500000}\pi \sqrt{0.01493943}$$

The equation is in standard form.

$$2.405x=\frac{43\pi \sqrt{0.01493943}}{2500000}$$

Divide both sides of the equation by 2.405, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{2.405x}{2.405}=\frac{43\pi \sqrt{1493943}}{2.405\times 25000000000}$$

Dividing by 2.405 undoes the multiplication by 2.405.

$$x=\frac{43\pi \sqrt{1493943}}{2.405\times 25000000000}$$

Divide \frac{43\pi \sqrt{1493943}}{25000000000} by 2.405 by multiplying \frac{43\pi \sqrt{1493943}}{25000000000} by the reciprocal of 2.405.

$$x=\frac{43\pi \sqrt{1493943}}{60125000000}$$

Variable x cannot be equal to 0.

$$x=\frac{43\pi \sqrt{1493943}}{60125000000}\text{, }x\neq 0$$