What are the solutions to the equation 20x^3-15x=3 ?

The solutions to the equation 20x^3-15x=3 are x\approx-0.21285…,x\approx-0.73974…,x\approx 0.95260…

Find the zeros of 20x^3-15x=3

The zeros of 20x^3-15x=3 are x\approx-0.21285…,x\approx-0.73974…,x\approx 0.95260…

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20 x^{3} - 15 x = 3

x \approx - 0.21285 \dots, x \approx - 0.73974 \dots, x \approx 0.95260 \dots

Solution steps

20 x^{3} - 15 x = 3

Move

3

to the left side

20 x^{3} - 15 x - 3 = 0

Find one solution for

20 x^{3} - 15 x - 3 = 0

using Newton-Raphson:

x \approx - 0.21285 \dots

Apply long division:

\frac{20 x ^{3} - 15 x - 3}{x + 0.21285 \dots} = 20 x^{2} - 4.25718 \dots x - 14.09381 \dots

20 x^{2} - 4.25718 \dots x - 14.09381 \dots \approx 0

Find one solution for

20 x^{2} - 4.25718 \dots x - 14.09381 \dots = 0

using Newton-Raphson:

x \approx - 0.73974 \dots

Apply long division:

\frac{20 x ^{2} - 4.25718 \dots x - 14.09381 \dots}{x + 0.73974 \dots} = 20 x - 19.05216 \dots

20 x - 19.05216 \dots \approx 0

x \approx 0.95260 \dots

The solutions are

x \approx - 0.21285 \dots, x \approx - 0.73974 \dots, x \approx 0.95260 \dots

(x^{2} - x - 3)^{2} - 2 (x^{2} - x) + 3 = 0

10 = x^{10}

r^{4} + 1 = 0

16 x^{4} - 36 x^{3} + 8 x^{2} = 0

a x^{4} = 4

What are the solutions to the equation 20x^3-15x=3 ?
The solutions to the equation 20x^3-15x=3 are x\approx-0.21285…,x\approx-0.73974…,x\approx 0.95260…
Find the zeros of 20x^3-15x=3
The zeros of 20x^3-15x=3 are x\approx-0.21285…,x\approx-0.73974…,x\approx 0.95260…