What are the solutions to the equation 10x^2-15=3x(6x^2-5x) ?

The solutions to the equation 10x^2-15=3x(6x^2-5x) are x\approx-0.64076…

Find the zeros of 10x^2-15=3x(6x^2-5x)

The zeros of 10x^2-15=3x(6x^2-5x) are x\approx-0.64076…

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10 x^{2} - 15 = 3 x (6 x^{2} - 5 x)

x \approx - 0.64076 \dots

Solution steps

10 x^{2} - 15 = 3 x (6 x^{2} - 5 x)

Expand

3 x (6 x^{2} - 5 x) : 18 x^{3} - 15 x^{2}

10 x^{2} - 15 = 18 x^{3} - 15 x^{2}

Switch sides

18 x^{3} - 15 x^{2} = 10 x^{2} - 15

Move

15

to the left side

18 x^{3} - 15 x^{2} + 15 = 10 x^{2}

Move

10 x^{2}

to the left side

18 x^{3} - 25 x^{2} + 15 = 0

Find one solution for

18 x^{3} - 25 x^{2} + 15 = 0

using Newton-Raphson:

x \approx - 0.64076 \dots

Apply long division:

\frac{18 x ^{3} - 25 x ^{2} + 15}{x + 0.64076 \dots} = 18 x^{2} - 36.53376 \dots x + 23.40953 \dots

18 x^{2} - 36.53376 \dots x + 23.40953 \dots \approx 0

Find one solution for

18 x^{2} - 36.53376 \dots x + 23.40953 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solution is

x \approx - 0.64076 \dots

1 = x^{5}

x^{4} + 8 x^{3} + 17 x^{2} - 2 x - 24 = 0

3 m^{3} - 12 m = 0

x^{3} - 4 x^{2} + 19 x + 5 = 0

(x^{4} - 3 x^{3} - 2 x^{2} - 3 x + 1) = 0

What are the solutions to the equation 10x^2-15=3x(6x^2-5x) ?
The solutions to the equation 10x^2-15=3x(6x^2-5x) are x\approx-0.64076…
Find the zeros of 10x^2-15=3x(6x^2-5x)
The zeros of 10x^2-15=3x(6x^2-5x) are x\approx-0.64076…