What are the solutions to the equation 5y^3+17y-12=9y^2-9y ?

The solutions to the equation 5y^3+17y-12=9y^2-9y are y\approx 0.53017…

Find the zeros of 5y^3+17y-12=9y^2-9y

The zeros of 5y^3+17y-12=9y^2-9y are y\approx 0.53017…

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5 y^{3} + 17 y - 12 = 9 y^{2} - 9 y

y \approx 0.53017 \dots

Solution steps

5 y^{3} + 17 y - 12 = 9 y^{2} - 9 y

Move

9 y

to the left side

5 y^{3} + 26 y - 12 = 9 y^{2}

Move

9 y^{2}

to the left side

5 y^{3} + 26 y - 12 - 9 y^{2} = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

5 y^{3} - 9 y^{2} + 26 y - 12 = 0

Find one solution for

5 y^{3} - 9 y^{2} + 26 y - 12 = 0

using Newton-Raphson:

y \approx 0.53017 \dots

Apply long division:

\frac{5 y ^{3} - 9 y ^{2} + 26 y - 12}{y - 0.53017 \dots} = 5 y^{2} - 6.34910 \dots y + 22.63383 \dots

5 y^{2} - 6.34910 \dots y + 22.63383 \dots \approx 0

Find one solution for

5 y^{2} - 6.34910 \dots y + 22.63383 \dots = 0

using Newton-Raphson:

No Solution for

y \in R

The solution is

y \approx 0.53017 \dots

4 x + 3 = x^{3} + 3 x^{2} - 9 x - 12

x^{3} - x^{2} - 5 x - 3 = 0

5 x^{3} + 23 x^{2} + 20 x - 12 = 0

x^{3} - x - 3360 = 0

b^{3} + 2 b^{2} - 10 b - 19 = 0

What are the solutions to the equation 5y^3+17y-12=9y^2-9y ?
The solutions to the equation 5y^3+17y-12=9y^2-9y are y\approx 0.53017…
Find the zeros of 5y^3+17y-12=9y^2-9y
The zeros of 5y^3+17y-12=9y^2-9y are y\approx 0.53017…