Solve y-200/y+20=10^-4.3

$$\frac { y - 200 } { y + 20 } = 10 ^ { - 4.3 }$$

Solve for y

$$y = \frac{20 {(100000 \cdot 10 ^ {0.3} + 1)}}{10000 \cdot 10 ^ {0.3} - 1} \approx 200.011026672$$

Steps for Solving Linear Equation

Variable y cannot be equal to -20 since division by zero is not defined. Multiply both sides of the equation by y+20.

$$y-200=\left(y+20\right)\times 10^{-4.3}$$

Use the distributive property to multiply y+20 by 10^{-4.3}.

$$y-200=y\times 10^{-4.3}+20\times 10^{-4.3}$$

Subtract y\times 10^{-4.3} from both sides.

$$y-200-y\times 10^{-4.3}=20\times 10^{-4.3}$$

Add 200 to both sides.

$$y-y\times 10^{-4.3}=20\times 10^{-4.3}+200$$

Combine all terms containing y.

$$\left(1-10^{-4.3}\right)y=20\times 10^{-4.3}+200$$

The equation is in standard form.

$$\left(-\frac{10^{0.7}}{100000}+1\right)y=\frac{10^{0.7}}{5000}+200$$

Divide both sides by 1-\frac{1}{100000}\times 10^{0.7}.

$$\frac{\left(-\frac{10^{0.7}}{100000}+1\right)y}{-\frac{10^{0.7}}{100000}+1}=\frac{\frac{10^{0.7}}{5000}+200}{-\frac{10^{0.7}}{100000}+1}$$

Dividing by 1-\frac{1}{100000}\times 10^{0.7} undoes the multiplication by 1-\frac{1}{100000}\times 10^{0.7}.

$$y=\frac{\frac{10^{0.7}}{5000}+200}{-\frac{10^{0.7}}{100000}+1}$$

Divide \frac{10^{0.7}}{5000}+200 by 1-\frac{1}{100000}\times 10^{0.7}.

$$y=-\frac{2\left(10^{0.7}+100000\right)\left(10^{0.7}+1000000\right)}{10^{0.4}-1000000000}$$