Solve 4x^5(2x-9)=3x^4

Question

Solve the equation

x_{1} = \frac{9 - 87}{4}, x_{2} = 0, x_{3} = \frac{9 + 87}{4}

Alternative Form

x_{1} \approx - 0.081845, x_{2} = 0, x_{3} \approx 4.581845

Evaluate

4 x^{5} (2 x - 9) = 3 x^{4}

Expand the expression

More Steps

8 x^{6} - 36 x^{5} = 3 x^{4}

Move the expression to the left side

8 x^{6} - 36 x^{5} - 3 x^{4} = 0

Factor the expression

x^{4} (8 x^{2} - 36 x - 3) = 0

Separate the equation into 2 possible cases

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

The only way a power can be 0 is when the base equals 0

x = 0 8 x^{2} - 36 x - 3 = 0

Solve the equation

More Steps

x = 0 x = \frac{9 + 87}{4} x = \frac{9 - 87}{4}

Solution

x_{1} = \frac{9 - 87}{4}, x_{2} = 0, x_{3} = \frac{9 + 87}{4}

Alternative Form

x_{1} \approx - 0.081845, x_{2} = 0, x_{3} \approx 4.581845

Show Solution