Solve 1000=1.2y/2sqrt{9.96*10^6}(1-1/sqrt{1+frac{0.05{pi0.8^2}}})

$$1000=1.2 \frac{ y }{ 2 } \sqrt{ 9.96 \times { 10 }^{ 6 } } (1- \frac{ 1 }{ \sqrt{ 1+ \frac{ 0.05 }{ \pi { 0.8 }^{ 2 } } } } )$$

Solve for y

$$y = \frac{320 \sqrt{249 \pi + 19.453125} {(\sqrt{\pi + 0.078125} + \sqrt{\pi})}}{747} \approx 43.263140736$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2000=1.2y\sqrt{9.96\times 10^{6}}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.8^{2}}}}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$2000=1.2y\sqrt{9.96\times 1000000}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.8^{2}}}}\right)$$

Multiply 9.96 and 1000000 to get 9960000.

$$2000=1.2y\sqrt{9960000}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.8^{2}}}}\right)$$

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}.

$$2000=1.2y\times 200\sqrt{249}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.8^{2}}}}\right)$$

Multiply 1.2 and 200 to get 240.

$$2000=240y\sqrt{249}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.8^{2}}}}\right)$$

Calculate 0.8 to the power of 2 and get 0.64.

$$2000=240y\sqrt{249}\left(1-\frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.64}}}\right)$$

Use the distributive property to multiply 240y\sqrt{249} by 1-\frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.64}}}.

$$2000=240y\sqrt{249}+240y\sqrt{249}\left(-\frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.64}}}\right)$$

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

$$240y\sqrt{249}+240y\sqrt{249}\left(-\frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.64}}}\right)=2000$$

Multiply 240 and -1 to get -240.

$$240y\sqrt{249}-240y\sqrt{249}\times \frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.64}}}=2000$$

Combine all terms containing y.

$$\left(240\sqrt{249}-240\sqrt{249}\times \frac{1}{\sqrt{1+\frac{0.05}{\pi \times 0.64}}}\right)y=2000$$

The equation is in standard form.

$$\left(-\frac{240\sqrt{249}}{\sqrt{\frac{5}{64\pi }+1}}+240\sqrt{249}\right)y=2000$$

Divide both sides by 240\sqrt{249}-240\sqrt{249}\left(\sqrt{1+0.078125\pi ^{-1}}\right)^{-1}.

$$\frac{\left(-\frac{240\sqrt{249}}{\sqrt{\frac{5}{64\pi }+1}}+240\sqrt{249}\right)y}{-\frac{240\sqrt{249}}{\sqrt{\frac{5}{64\pi }+1}}+240\sqrt{249}}=\frac{2000}{-\frac{240\sqrt{249}}{\sqrt{\frac{5}{64\pi }+1}}+240\sqrt{249}}$$

Dividing by 240\sqrt{249}-240\sqrt{249}\left(\sqrt{1+0.078125\pi ^{-1}}\right)^{-1} undoes the multiplication by 240\sqrt{249}-240\sqrt{249}\left(\sqrt{1+0.078125\pi ^{-1}}\right)^{-1}.

$$y=\frac{2000}{-\frac{240\sqrt{249}}{\sqrt{\frac{5}{64\pi }+1}}+240\sqrt{249}}$$

Divide 2000 by 240\sqrt{249}-240\sqrt{249}\left(\sqrt{1+0.078125\pi ^{-1}}\right)^{-1}.

$$y=\frac{320\sqrt{249\pi +19.453125}\left(\sqrt{\pi +0.078125}+\sqrt{\pi }\right)}{747}$$