Solve y=4x(1-3000/sqrt{9.96*10^6})-1

$$y=4x(1- \frac{ 3000 }{ \sqrt{ 9.96 \times { 10 }^{ 6 } } } )-1$$

Solve for x

$$x=\frac{\left(5\sqrt{249}+83\right)\left(y+1\right)}{32}$$

Steps for Solving Linear Equation

Calculate 10 to the power of 6 and get 1000000.

$$y=4x\left(1-\frac{3000}{\sqrt{9.96\times 1000000}}\right)-1$$

Multiply 9.96 and 1000000 to get 9960000.

$$y=4x\left(1-\frac{3000}{\sqrt{9960000}}\right)-1$$

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}.

$$y=4x\left(1-\frac{3000}{200\sqrt{249}}\right)-1$$

Rationalize the denominator of \frac{3000}{200\sqrt{249}} by multiplying numerator and denominator by \sqrt{249}.

$$y=4x\left(1-\frac{3000\sqrt{249}}{200\left(\sqrt{249}\right)^{2}}\right)-1$$

The square of \sqrt{249} is 249.

$$y=4x\left(1-\frac{3000\sqrt{249}}{200\times 249}\right)-1$$

Cancel out 3\times 200 in both numerator and denominator.

$$y=4x\left(1-\frac{5\sqrt{249}}{83}\right)-1$$

Use the distributive property to multiply 4x by 1-\frac{5\sqrt{249}}{83}.

$$y=4x+4x\left(-\frac{5\sqrt{249}}{83}\right)-1$$

Express 4\left(-\frac{5\sqrt{249}}{83}\right) as a single fraction.

$$y=4x+\frac{-4\times 5\sqrt{249}}{83}x-1$$

Multiply -4 and 5 to get -20.

$$y=4x+\frac{-20\sqrt{249}}{83}x-1$$

Express \frac{-20\sqrt{249}}{83}x as a single fraction.

$$y=4x+\frac{-20\sqrt{249}x}{83}-1$$

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

$$4x+\frac{-20\sqrt{249}x}{83}-1=y$$

Add 1 to both sides.

$$4x+\frac{-20\sqrt{249}x}{83}=y+1$$

Multiply both sides of the equation by 83.

$$332x-20\sqrt{249}x=83y+83$$

Combine all terms containing x.

$$\left(332-20\sqrt{249}\right)x=83y+83$$

Divide both sides by 332-20\sqrt{249}.

$$\frac{\left(332-20\sqrt{249}\right)x}{332-20\sqrt{249}}=\frac{83y+83}{332-20\sqrt{249}}$$

Dividing by 332-20\sqrt{249} undoes the multiplication by 332-20\sqrt{249}.

$$x=\frac{83y+83}{332-20\sqrt{249}}$$

Divide 83+83y by 332-20\sqrt{249}.

$$x=\frac{\left(5\sqrt{249}+83\right)\left(y+1\right)}{32}$$

Solve for y

$$y=-\frac{20\sqrt{249}x}{83}+4x-1$$