Solve 1200x+400x=sqrt{3x}

$$1200 x + 400 x = \sqrt { 3 x }$$

Solve for x

$$x=\frac{3}{2560000}=0.000001172$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(1200x+400x\right)^{2}=\left(\sqrt{3x}\right)^{2}$$

Combine 1200x and 400x to get 1600x.

$$\left(1600x\right)^{2}=\left(\sqrt{3x}\right)^{2}$$

Expand \left(1600x\right)^{2}.

$$1600^{2}x^{2}=\left(\sqrt{3x}\right)^{2}$$

Calculate 1600 to the power of 2 and get 2560000.

$$2560000x^{2}=\left(\sqrt{3x}\right)^{2}$$

Calculate \sqrt{3x} to the power of 2 and get 3x.

$$2560000x^{2}=3x$$

Subtract 3x from both sides.

$$2560000x^{2}-3x=0$$

Factor out x.

$$x\left(2560000x-3\right)=0$$

To find equation solutions, solve x=0 and 2560000x-3=0.

$$x=0 x=\frac{3}{2560000}$$

Substitute 0 for x in the equation 1200x+400x=\sqrt{3x}.

$$1200\times 0+400\times 0=\sqrt{3\times 0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Substitute \frac{3}{2560000} for x in the equation 1200x+400x=\sqrt{3x}.

$$1200\times \frac{3}{2560000}+400\times \frac{3}{2560000}=\sqrt{3\times \frac{3}{2560000}}$$

Simplify. The value x=\frac{3}{2560000} satisfies the equation.

$$\frac{3}{1600}=\frac{3}{1600}$$

List all solutions of 400x+1200x=\sqrt{3x}.

$$x=0 x=\frac{3}{2560000}$$