Sure it is possible, but L will be in terms of Q only.
Q = 10L - 1/2000 (L)squared
I assume the -1/2000 (L)squared is -(1/2000)(L^2) so that the given
equation is quadratic only.
[If it were -1/(2000 L^2), then the given equation would be cubic.]
Q = 10L -(1/2000)(L^2)
Q = 10L -0.0005(L^2)
Put them all to the lefthand side,
0.0005(L^2) -10L +Q = 0
Use the Quadratic Formula,
L = {-(-10) +,-sqrt[(-10)^2 -4(0.0005)(Q)]} / (2* 0.0005)
L = {10 +,-sqrt[100 -(0.002)Q]} / 0.001
L = 10,000 +,-1000sqrt[100 -0.002Q]
That means,
L = 10,000 +1000sqrt[100 -0.002Q] ----***
or,
L = 10,000 -1000sqrt[100 -0.002Q] ----***
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