Solve 0.6=2x(1-0.6/1+0.6-263/sqrt{9.96*10^6})-1

$$0.6=2x( \frac{ 1-0.6 }{ 1+0.6 } - \frac{ 263 }{ \sqrt{ 9.96 \times { 10 }^{ 6 } } } )-1$$

Solve for x

$$x = \frac{42080 \sqrt{249} + 1992000}{553331} \approx 4.800040482$$

Steps for Solving Linear Equation

Subtract 0.6 from 1 to get 0.4.

$$0.6=2x\left(\frac{0.4}{1+0.6}-\frac{263}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Add 1 and 0.6 to get 1.6.

$$0.6=2x\left(\frac{0.4}{1.6}-\frac{263}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Expand \frac{0.4}{1.6} by multiplying both numerator and the denominator by 10.

$$0.6=2x\left(\frac{4}{16}-\frac{263}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Reduce the fraction \frac{4}{16} to lowest terms by extracting and canceling out 4.

$$0.6=2x\left(\frac{1}{4}-\frac{263}{\sqrt{9.96\times 10^{6}}}\right)-1$$

Calculate 10 to the power of 6 and get 1000000.

$$0.6=2x\left(\frac{1}{4}-\frac{263}{\sqrt{9.96\times 1000000}}\right)-1$$

Multiply 9.96 and 1000000 to get 9960000.

$$0.6=2x\left(\frac{1}{4}-\frac{263}{\sqrt{9960000}}\right)-1$$

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}.

$$0.6=2x\left(\frac{1}{4}-\frac{263}{200\sqrt{249}}\right)-1$$

Rationalize the denominator of \frac{263}{200\sqrt{249}} by multiplying numerator and denominator by \sqrt{249}.

$$0.6=2x\left(\frac{1}{4}-\frac{263\sqrt{249}}{200\left(\sqrt{249}\right)^{2}}\right)-1$$

The square of \sqrt{249} is 249.

$$0.6=2x\left(\frac{1}{4}-\frac{263\sqrt{249}}{200\times 249}\right)-1$$

Multiply 200 and 249 to get 49800.

$$0.6=2x\left(\frac{1}{4}-\frac{263\sqrt{249}}{49800}\right)-1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 49800 is 49800. Multiply \frac{1}{4} times \frac{12450}{12450}.

$$0.6=2x\left(\frac{12450}{49800}-\frac{263\sqrt{249}}{49800}\right)-1$$

Since \frac{12450}{49800} and \frac{263\sqrt{249}}{49800} have the same denominator, subtract them by subtracting their numerators.

$$0.6=2x\times \frac{12450-263\sqrt{249}}{49800}-1$$

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

$$0.6=\frac{12450-263\sqrt{249}}{24900}x-1$$

Divide each term of 12450-263\sqrt{249} by 24900 to get \frac{1}{2}-\frac{263}{24900}\sqrt{249}.

$$0.6=\left(\frac{1}{2}-\frac{263}{24900}\sqrt{249}\right)x-1$$

Use the distributive property to multiply \frac{1}{2}-\frac{263}{24900}\sqrt{249} by x.

$$0.6=\frac{1}{2}x-\frac{263}{24900}\sqrt{249}x-1$$

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

$$\frac{1}{2}x-\frac{263}{24900}\sqrt{249}x-1=0.6$$

Add 1 to both sides.

$$\frac{1}{2}x-\frac{263}{24900}\sqrt{249}x=0.6+1$$

Add 0.6 and 1 to get 1.6.

$$\frac{1}{2}x-\frac{263}{24900}\sqrt{249}x=1.6$$

Combine all terms containing x.

$$\left(\frac{1}{2}-\frac{263}{24900}\sqrt{249}\right)x=1.6$$

The equation is in standard form.

$$\left(-\frac{263\sqrt{249}}{24900}+\frac{1}{2}\right)x=\frac{8}{5}$$

Divide both sides by \frac{1}{2}-\frac{263}{24900}\sqrt{249}.

$$\frac{\left(-\frac{263\sqrt{249}}{24900}+\frac{1}{2}\right)x}{-\frac{263\sqrt{249}}{24900}+\frac{1}{2}}=\frac{\frac{8}{5}}{-\frac{263\sqrt{249}}{24900}+\frac{1}{2}}$$

Dividing by \frac{1}{2}-\frac{263}{24900}\sqrt{249} undoes the multiplication by \frac{1}{2}-\frac{263}{24900}\sqrt{249}.

$$x=\frac{\frac{8}{5}}{-\frac{263\sqrt{249}}{24900}+\frac{1}{2}}$$

Divide \frac{8}{5} by \frac{1}{2}-\frac{263}{24900}\sqrt{249}.

$$x=\frac{42080\sqrt{249}+1992000}{553331}$$