Solve sqrt{6a-5}-sqrt{4a+8}=0

$$\sqrt { 6 a - 5 } - \sqrt { 4 a + 8 } = 0$$

Solve for a

$$a = \frac{13}{2} = 6\frac{1}{2} = 6.5$$

Solution Steps

Subtract -\sqrt{4a+8} from both sides of the equation.

$$\sqrt{6a-5}=\sqrt{4a+8}$$

Square both sides of the equation.

$$\left(\sqrt{6a-5}\right)^{2}=\left(\sqrt{4a+8}\right)^{2}$$

Calculate \sqrt{6a-5} to the power of 2 and get 6a-5.

$$6a-5=\left(\sqrt{4a+8}\right)^{2}$$

Calculate \sqrt{4a+8} to the power of 2 and get 4a+8.

$$6a-5=4a+8$$

Subtract 4a from both sides.

$$6a-5-4a=8$$

Combine 6a and -4a to get 2a.

$$2a-5=8$$

Add 5 to both sides.

$$2a=8+5$$

Add 8 and 5 to get 13.

$$2a=13$$

Divide both sides by 2.

$$a=\frac{13}{2}$$

Substitute \frac{13}{2} for a in the equation \sqrt{6a-5}-\sqrt{4a+8}=0.

$$\sqrt{6\times \frac{13}{2}-5}-\sqrt{4\times \frac{13}{2}+8}=0$$

Simplify. The value a=\frac{13}{2} satisfies the equation.

$$0=0$$

Equation \sqrt{6a-5}=\sqrt{4a+8} has a unique solution.

$$a=\frac{13}{2}$$