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Answer:
h = (1 -2u² ± √(1 -4u²-12u⁴))/g
Step-by-step explanation:
This is a quadratic in h, so there are two solutions.
Written in standard form, the given equation is ...
(-g/2)h² +(1-2u²)h -8u⁴/g = 0
The quadratic formula tells you the solution for h is ...
h = (-(1 -2u²) ±√((1 -2u²) -4(-g/2)(-8u⁴/g)))/(2(-g/2))
h = (2u² -1 ± √(4u⁴ -4u² +1 -16u⁴))/-g . . . . . simplify
h = (1 -2u² ± √(1 -4u²-12u⁴))/g . . . . . . . . collect terms
