What are the solutions to the equation 38=h(2h^2-3h) ?

The solutions to the equation 38=h(2h^2-3h) are h\approx 3.27329…

Find the zeros of 38=h(2h^2-3h)

The zeros of 38=h(2h^2-3h) are h\approx 3.27329…

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38 = h (2 h^{2} - 3 h)

h \approx 3.27329 \dots

Solution steps

38 = h (2 h^{2} - 3 h)

Expand

h (2 h^{2} - 3 h) : 2 h^{3} - 3 h^{2}

38 = 2 h^{3} - 3 h^{2}

Switch sides

2 h^{3} - 3 h^{2} = 38

Move

38

to the left side

2 h^{3} - 3 h^{2} - 38 = 0

Find one solution for

2 h^{3} - 3 h^{2} - 38 = 0

using Newton-Raphson:

h \approx 3.27329 \dots

Apply long division:

\frac{2 h ^{3} - 3 h ^{2} - 38}{h - 3.27329 \dots} = 2 h^{2} + 3.54659 \dots h + 11.60908 \dots

2 h^{2} + 3.54659 \dots h + 11.60908 \dots \approx 0

Find one solution for

2 h^{2} + 3.54659 \dots h + 11.60908 \dots = 0

using Newton-Raphson:

No Solution for

h \in R

The solution is

h \approx 3.27329 \dots

(y - 1) (y^{2} + y + 2) = 0

5 = 3 - \frac{1}{10} b^{3} - 101 b

- 6 x^{3} + 36 x^{2} + 42 x = 0

x^{3} - 4 x + 3 = 2.8

x^{3} x = 18

What are the solutions to the equation 38=h(2h^2-3h) ?
The solutions to the equation 38=h(2h^2-3h) are h\approx 3.27329…
Find the zeros of 38=h(2h^2-3h)
The zeros of 38=h(2h^2-3h) are h\approx 3.27329…