To solve this equation, we first multiply both sides by (X + 10) to eliminate the fraction:

(X0.5714 + 10) = 0.6939(X + 10)

Next, distribute the 0.6939 on the right side:

X*0.5714 + 10 = 0.6939X + 6.939

Next, move the terms involving X to one side:

X*0.5714 - 0.6939X = 6.939 - 10
X(0.5714 - 0.6939) = -3.061
-0.1225X = -3.061

Finally, solve for X:

X = -3.061 / -0.1225
X = 25

Therefore, the solution to the equation is X = 25.