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20/(x-14)=14/(x-20) equation
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The solution
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20 14 ------ = ------ x - 14 x - 20
$$\frac{20}{x - 14} = \frac{14}{x - 20}$$
Detail solution
Given the equation:
$$\frac{20}{x - 14} = \frac{14}{x - 20}$$
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
so we get the equation
$$20 \left(x - 20\right) = 14 \left(x - 14\right)$$
$$20 x - 400 = 14 x - 196$$
Move free summands (without x)
from left part to right part, we given:
$$20 x = 14 x + 204$$
Move the summands with the unknown x
from the right part to the left part:
$$6 x = 204$$
Divide both parts of the equation by 6
We get the answer: x = 34
$$\frac{20}{x - 14} = \frac{14}{x - 20}$$
Use proportions rule:
From a1/b1 = a2/b2 should a1*b2 = a2*b1,
In this case
a1 = 20
b1 = -14 + x
a2 = 14
b2 = -20 + x
so we get the equation
$$20 \left(x - 20\right) = 14 \left(x - 14\right)$$
$$20 x - 400 = 14 x - 196$$
Move free summands (without x)
from left part to right part, we given:
$$20 x = 14 x + 204$$
Move the summands with the unknown x
from the right part to the left part:
$$6 x = 204$$
Divide both parts of the equation by 6
x = 204 / (6)
We get the answer: x = 34