What is the answer to h^{1.5}(2-4h)=6h ?

The answer to h^{1.5}(2-4h)=6h is h=0

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h^{1.5}(2-4h)=6h

h^{1.5} (2 - 4 h) = 6 h

h = 0

Solution steps

h^{1.5} (2 - 4 h) = 6 h

Expand

h^{1.5} (2 - 4 h) : 2 h^{1.5} - 4 h^{1.5} h

2 h^{1.5} - 4 h^{1.5} h = 6 h

Factor

2 h^{1.5} - 4 h^{1.5} h : 2 h^{1.5} (1 - 2 h)

2 h^{1.5} (1 - 2 h) = 6 h

Take both sides of the equation to the power of

2 : 4 h^{3} - 16 h^{4} + 16 h^{5} = 36 h^{2}

4 h^{3} - 16 h^{4} + 16 h^{5} = 36 h^{2}

Solve

4 h^{3} - 16 h^{4} + 16 h^{5} = 36 h^{2} : h = 0, h \approx 1.66312 \dots

h = 0, h \approx 1.66312 \dots

Verify Solutions:

h = 0

True

, h \approx 1.66312 \dots

False

The solution is

h = 0

2 x^{2} = - 3 + 7 x

- 7 \cdot x = - 25 - x^{2}

2 - \frac{2}{x ^{\frac{1}{3}}} = 0

0 = 2 \cdot 3 π t^{\frac{1}{5}}

5 x - 3 - 3 = 0