Solve sqrt{4u+7}=sqrt{6u-15}

$$\sqrt { 4 u + 7 } = \sqrt { 6 u - 15 }$$

Solve for u

$$u=11$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{4u+7}\right)^{2}=\left(\sqrt{6u-15}\right)^{2}$$

Calculate \sqrt{4u+7} to the power of 2 and get 4u+7.

$$4u+7=\left(\sqrt{6u-15}\right)^{2}$$

Calculate \sqrt{6u-15} to the power of 2 and get 6u-15.

$$4u+7=6u-15$$

Subtract 6u from both sides.

$$4u+7-6u=-15$$

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

$$-2u+7=-15$$

Subtract 7 from both sides.

$$-2u=-15-7$$

Subtract 7 from -15 to get -22.

$$-2u=-22$$

Divide both sides by -2.

$$u=\frac{-22}{-2}$$

Divide -22 by -2 to get 11.

$$u=11$$

Substitute 11 for u in the equation \sqrt{4u+7}=\sqrt{6u-15}.

$$\sqrt{4\times 11+7}=\sqrt{6\times 11-15}$$

Simplify. The value u=11 satisfies the equation.

$$51^{\frac{1}{2}}=51^{\frac{1}{2}}$$

Equation \sqrt{4u+7}=\sqrt{6u-15} has a unique solution.

$$u=11$$