What are the solutions to the equation 3v+126=4v^3 ?

The solutions to the equation 3v+126=4v^3 are v\approx 3.23732…

Find the zeros of 3v+126=4v^3

The zeros of 3v+126=4v^3 are v\approx 3.23732…

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3 v + 126 = 4 v^{3}

v \approx 3.23732 \dots

Solution steps

3 v + 126 = 4 v^{3}

Switch sides

4 v^{3} = 3 v + 126

Move

126

to the left side

4 v^{3} - 126 = 3 v

Move

3 v

to the left side

4 v^{3} - 126 - 3 v = 0

Write in the standard form

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

4 v^{3} - 3 v - 126 = 0

Find one solution for

4 v^{3} - 3 v - 126 = 0

using Newton-Raphson:

v \approx 3.23732 \dots

Apply long division:

\frac{4 v ^{3} - 3 v - 126}{v - 3.23732 \dots} = 4 v^{2} + 12.94929 \dots v + 38.92104 \dots

4 v^{2} + 12.94929 \dots v + 38.92104 \dots \approx 0

Find one solution for

4 v^{2} + 12.94929 \dots v + 38.92104 \dots = 0

using Newton-Raphson:

No Solution for

v \in R

The solution is

v \approx 3.23732 \dots

25 x^{4} - 3 = 13

64 x^{3} - 112 x^{2} - 4 x + 7 = 0

20 x^{3} - 108 x^{2} + 162 x - 54 = 0

2 = x^{3} + 2 x - 1

3 x^{3} - x = 0

What are the solutions to the equation 3v+126=4v^3 ?
The solutions to the equation 3v+126=4v^3 are v\approx 3.23732…
Find the zeros of 3v+126=4v^3
The zeros of 3v+126=4v^3 are v\approx 3.23732…