Solve 0.2=2y(1-0.2/1+0.2-x/sqrt{9.96*10^6})-1

$$0.2=2y( \frac{ 1-0.2 }{ 1+0.2 } - \frac{ x }{ \sqrt{ 9.96 \times { 10 }^{ 6 } } } )-1$$

Solve for x

$$x=\frac{40\sqrt{249}\left(10y-9\right)}{3y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Subtract 0.2 from 1 to get 0.8.

$$0.2=2y\left(\frac{0.8}{1+0.2}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Add 1 and 0.2 to get 1.2.

$$0.2=2y\left(\frac{0.8}{1.2}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Expand \frac{0.8}{1.2} by multiplying both numerator and the denominator by 10.

$$0.2=2y\left(\frac{8}{12}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$0.2=2y\left(\frac{2}{3}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Calculate 10 to the power of 6 and get 1000000.

$$0.2=2y\left(\frac{2}{3}-\frac{x}{\sqrt{9.96\times 1000000}}\right)-1$$

Multiply 9.96 and 1000000 to get 9960000.

$$0.2=2y\left(\frac{2}{3}-\frac{x}{\sqrt{9960000}}\right)-1$$

Factor 9960000=200^{2}\times 249. Rewrite the square root of the product \sqrt{200^{2}\times 249} as the product of square roots \sqrt{200^{2}}\sqrt{249}. Take the square root of 200^{2}.

$$0.2=2y\left(\frac{2}{3}-\frac{x}{200\sqrt{249}}\right)-1$$

Rationalize the denominator of \frac{x}{200\sqrt{249}} by multiplying numerator and denominator by \sqrt{249}.

$$0.2=2y\left(\frac{2}{3}-\frac{x\sqrt{249}}{200\left(\sqrt{249}\right)^{2}}\right)-1$$

The square of \sqrt{249} is 249.

$$0.2=2y\left(\frac{2}{3}-\frac{x\sqrt{249}}{200\times 249}\right)-1$$

Multiply 200 and 249 to get 49800.

$$0.2=2y\left(\frac{2}{3}-\frac{x\sqrt{249}}{49800}\right)-1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 49800 is 49800. Multiply \frac{2}{3} times \frac{16600}{16600}.

$$0.2=2y\left(\frac{2\times 16600}{49800}-\frac{x\sqrt{249}}{49800}\right)-1$$

Since \frac{2\times 16600}{49800} and \frac{x\sqrt{249}}{49800} have the same denominator, subtract them by subtracting their numerators.

$$0.2=2y\times \frac{2\times 16600-x\sqrt{249}}{49800}-1$$

Do the multiplications in 2\times 16600-x\sqrt{249}.

$$0.2=2y\times \frac{33200-x\sqrt{249}}{49800}-1$$

Cancel out 49800, the greatest common factor in 2 and 49800.

$$0.2=\frac{33200-x\sqrt{249}}{24900}y-1$$

Express \frac{33200-x\sqrt{249}}{24900}y as a single fraction.

$$0.2=\frac{\left(33200-x\sqrt{249}\right)y}{24900}-1$$

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

$$\frac{\left(33200-x\sqrt{249}\right)y}{24900}-1=0.2$$

Use the distributive property to multiply 33200-x\sqrt{249} by y.

$$\frac{33200y-x\sqrt{249}y}{24900}-1=0.2$$

Add 1 to both sides.

$$\frac{33200y-x\sqrt{249}y}{24900}=0.2+1$$

Add 0.2 and 1 to get 1.2.

$$\frac{33200y-x\sqrt{249}y}{24900}=1.2$$

Multiply both sides by 24900.

$$33200y-x\sqrt{249}y=1.2\times 24900$$

Multiply 1.2 and 24900 to get 29880.

$$33200y-x\sqrt{249}y=29880$$

Subtract 33200y from both sides.

$$-x\sqrt{249}y=29880-33200y$$

The equation is in standard form.

$$\left(-\sqrt{249}y\right)x=29880-33200y$$

Divide both sides by -\sqrt{249}y.

$$\frac{\left(-\sqrt{249}y\right)x}{-\sqrt{249}y}=\frac{29880-33200y}{-\sqrt{249}y}$$

Dividing by -\sqrt{249}y undoes the multiplication by -\sqrt{249}y.

$$x=\frac{29880-33200y}{-\sqrt{249}y}$$

Divide 29880-33200y by -\sqrt{249}y.

$$x=-\frac{40\sqrt{249}\left(9-10y\right)}{3y}$$

Solve for y

$$y=\frac{29880}{-\sqrt{249}x+33200}$$

$$x\neq \frac{400\sqrt{249}}{3}$$

Steps for Solving Linear Equation

Subtract 0.2 from 1 to get 0.8.

$$0.2=2y\left(\frac{0.8}{1+0.2}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Add 1 and 0.2 to get 1.2.

$$0.2=2y\left(\frac{0.8}{1.2}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Expand \frac{0.8}{1.2} by multiplying both numerator and the denominator by 10.

$$0.2=2y\left(\frac{8}{12}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$0.2=2y\left(\frac{2}{3}-\frac{x}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Calculate 10 to the power of 6 and get 1000000.

$$0.2=2y\left(\frac{2}{3}-\frac{x}{\sqrt{9.96\times 1000000}}\right)-1$$

Multiply 9.96 and 1000000 to get 9960000.

$$0.2=2y\left(\frac{2}{3}-\frac{x}{\sqrt{9960000}}\right)-1$$

Factor 9960000=200^{2}\times 249. Rewrite the square root of the product \sqrt{200^{2}\times 249} as the product of square roots \sqrt{200^{2}}\sqrt{249}. Take the square root of 200^{2}.

$$0.2=2y\left(\frac{2}{3}-\frac{x}{200\sqrt{249}}\right)-1$$

Rationalize the denominator of \frac{x}{200\sqrt{249}} by multiplying numerator and denominator by \sqrt{249}.

$$0.2=2y\left(\frac{2}{3}-\frac{x\sqrt{249}}{200\left(\sqrt{249}\right)^{2}}\right)-1$$

The square of \sqrt{249} is 249.

$$0.2=2y\left(\frac{2}{3}-\frac{x\sqrt{249}}{200\times 249}\right)-1$$

Multiply 200 and 249 to get 49800.

$$0.2=2y\left(\frac{2}{3}-\frac{x\sqrt{249}}{49800}\right)-1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 49800 is 49800. Multiply \frac{2}{3} times \frac{16600}{16600}.

$$0.2=2y\left(\frac{2\times 16600}{49800}-\frac{x\sqrt{249}}{49800}\right)-1$$

Since \frac{2\times 16600}{49800} and \frac{x\sqrt{249}}{49800} have the same denominator, subtract them by subtracting their numerators.

$$0.2=2y\times \frac{2\times 16600-x\sqrt{249}}{49800}-1$$

Do the multiplications in 2\times 16600-x\sqrt{249}.

$$0.2=2y\times \frac{33200-x\sqrt{249}}{49800}-1$$

Cancel out 49800, the greatest common factor in 2 and 49800.

$$0.2=\frac{33200-x\sqrt{249}}{24900}y-1$$

Express \frac{33200-x\sqrt{249}}{24900}y as a single fraction.

$$0.2=\frac{\left(33200-x\sqrt{249}\right)y}{24900}-1$$

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

$$\frac{\left(33200-x\sqrt{249}\right)y}{24900}-1=0.2$$

Use the distributive property to multiply 33200-x\sqrt{249} by y.

$$\frac{33200y-x\sqrt{249}y}{24900}-1=0.2$$

Add 1 to both sides.

$$\frac{33200y-x\sqrt{249}y}{24900}=0.2+1$$

Add 0.2 and 1 to get 1.2.

$$\frac{33200y-x\sqrt{249}y}{24900}=1.2$$

Multiply both sides by 24900.

$$33200y-x\sqrt{249}y=1.2\times 24900$$

Multiply 1.2 and 24900 to get 29880.

$$33200y-x\sqrt{249}y=29880$$

Combine all terms containing y.

$$\left(33200-x\sqrt{249}\right)y=29880$$

The equation is in standard form.

$$\left(-\sqrt{249}x+33200\right)y=29880$$

Divide both sides by 33200-x\sqrt{249}.

$$\frac{\left(-\sqrt{249}x+33200\right)y}{-\sqrt{249}x+33200}=\frac{29880}{-\sqrt{249}x+33200}$$

Dividing by 33200-x\sqrt{249} undoes the multiplication by 33200-x\sqrt{249}.

$$y=\frac{29880}{-\sqrt{249}x+33200}$$