Solve sqrt{4x-6}=sqrt{3-x}

$$\sqrt { 4 x - 6 } = \sqrt { 3 - x }$$

Solve for x

$$x = \frac{9}{5} = 1\frac{4}{5} = 1.8$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{4x-6}\right)^{2}=\left(\sqrt{3-x}\right)^{2}$$

Calculate \sqrt{4x-6} to the power of 2 and get 4x-6.

$$4x-6=\left(\sqrt{3-x}\right)^{2}$$

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

$$4x-6=3-x$$

Add x to both sides.

$$4x-6+x=3$$

Combine 4x and x to get 5x.

$$5x-6=3$$

Add 6 to both sides.

$$5x=3+6$$

Add 3 and 6 to get 9.

$$5x=9$$

Divide both sides by 5.

$$x=\frac{9}{5}$$

Substitute \frac{9}{5} for x in the equation \sqrt{4x-6}=\sqrt{3-x}.

$$\sqrt{4\times \frac{9}{5}-6}=\sqrt{3-\frac{9}{5}}$$

Simplify. The value x=\frac{9}{5} satisfies the equation.

$$\frac{1}{5}\times 30^{\frac{1}{2}}=\frac{1}{5}\times 30^{\frac{1}{2}}$$

Equation \sqrt{4x-6}=\sqrt{3-x} has a unique solution.

$$x=\frac{9}{5}$$