Solve 0.86=frac{2767.5-h_{2}}{2767.5-1838.4}

$$0.86 = \frac { 2767.5 - h _ { 2 } } { 2767.5 - 1838.4 }$$

Solve for h_2

$$h_{2}=1968.474$$

Steps for Solving Linear Equation

Subtract 1838.4 from 2767.5 to get 929.1.

$$0.86=\frac{2767.5-h_{2}}{929.1}$$

Divide each term of 2767.5-h_{2} by 929.1 to get \frac{2767.5}{929.1}+\frac{-h_{2}}{929.1}.

$$0.86=\frac{2767.5}{929.1}+\frac{-h_{2}}{929.1}$$

Expand \frac{2767.5}{929.1} by multiplying both numerator and the denominator by 10.

$$0.86=\frac{27675}{9291}+\frac{-h_{2}}{929.1}$$

Reduce the fraction \frac{27675}{9291} to lowest terms by extracting and canceling out 3.

$$0.86=\frac{9225}{3097}+\frac{-h_{2}}{929.1}$$

Divide -h_{2} by 929.1 to get -\frac{10}{9291}h_{2}.

$$0.86=\frac{9225}{3097}-\frac{10}{9291}h_{2}$$

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

$$\frac{9225}{3097}-\frac{10}{9291}h_{2}=0.86$$

Subtract \frac{9225}{3097} from both sides.

$$-\frac{10}{9291}h_{2}=0.86-\frac{9225}{3097}$$

Convert decimal number 0.86 to fraction \frac{86}{100}. Reduce the fraction \frac{86}{100} to lowest terms by extracting and canceling out 2.

$$-\frac{10}{9291}h_{2}=\frac{43}{50}-\frac{9225}{3097}$$

Least common multiple of 50 and 3097 is 154850. Convert \frac{43}{50} and \frac{9225}{3097} to fractions with denominator 154850.

$$-\frac{10}{9291}h_{2}=\frac{133171}{154850}-\frac{461250}{154850}$$

Since \frac{133171}{154850} and \frac{461250}{154850} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{10}{9291}h_{2}=\frac{133171-461250}{154850}$$

Subtract 461250 from 133171 to get -328079.

$$-\frac{10}{9291}h_{2}=-\frac{328079}{154850}$$

Divide both sides by -\frac{10}{9291}.

$$h_{2}=\frac{-\frac{328079}{154850}}{-\frac{10}{9291}}$$

Express \frac{-\frac{328079}{154850}}{-\frac{10}{9291}} as a single fraction.

$$h_{2}=\frac{-328079}{154850\left(-\frac{10}{9291}\right)}$$

Multiply 154850 and -\frac{10}{9291} to get -\frac{500}{3}.

$$h_{2}=\frac{-328079}{-\frac{500}{3}}$$