Solve 15x^2-10\sqrt 6x 10=0

Question

Solve the equation

x_{1} = 0, x_{2} = \frac{2 3 90}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 2.987603

Evaluate

15 x^{2} - 10 6 x \times 10 = 0

Find the domain

More Steps

15 x^{2} - 10 6 x \times 10 = 0, x \geq 0

Multiply the terms

15 x^{2} - 10 60 x = 0

Move the expression to the right-hand side and change its sign

- 10 60 x = - 15 x^{2}

Divide both sides of the equation by - 5

2 60 x = 3 x^{2}

Rewrite the expression

60 x = \frac{3 x ^{2}}{2}

Raise both sides of the equation to the 2 -th power to eliminate the isolated 2 -th root

(60 x)^{2} = (\frac{3 x ^{2}}{2})^{2}

Evaluate the power

60 x = \frac{9 x ^{4}}{4}

Cross multiply

60 x \times 4 = 9 x^{4}

Simplify the equation

240 x = 9 x^{4}

Rewrite the expression

3 \times 80 x = 3 \times 3 x^{4}

Evaluate

80 x = 3 x^{4}

Add or subtract both sides

80 x - 3 x^{4} = 0

Factor the expression

x (80 - 3 x^{3}) = 0

Separate the equation into 2 possible cases

x = 0 80 - 3 x^{3} = 0

Solve the equation

More Steps

x = 0 x = \frac{2 3 90}{3}

Check if the solution is in the defined range

x = 0 x = \frac{2 3 90}{3}, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = \frac{2 3 90}{3}

Check the solution

More Steps

x = 0 x = \frac{2 3 90}{3}

Check the solution

More Steps

x = 0 x = \frac{2 3 90}{3}

Solution

x_{1} = 0, x_{2} = \frac{2 3 90}{3}

Alternative Form

x_{1} = 0, x_{2} \approx 2.987603

Show Solution