Solve 5sqrt{2}a+9=2sqrt{2}a+24

$$5 \sqrt { 2 } a + 9 = 2 \sqrt { 2 } a + 24$$

Solve for a

$$a = \frac{5 \sqrt{2}}{2} \approx 3.535533906$$

Steps for Solving Linear Equation

Subtract 2\sqrt{2}a from both sides.

$$5\sqrt{2}a+9-2\sqrt{2}a=24$$

Combine 5\sqrt{2}a and -2\sqrt{2}a to get 3\sqrt{2}a.

$$3\sqrt{2}a+9=24$$

Subtract 9 from both sides.

$$3\sqrt{2}a=24-9$$

Subtract 9 from 24 to get 15.

$$3\sqrt{2}a=15$$

Divide both sides by 3\sqrt{2}.

$$\frac{3\sqrt{2}a}{3\sqrt{2}}=\frac{15}{3\sqrt{2}}$$

Dividing by 3\sqrt{2} undoes the multiplication by 3\sqrt{2}.

$$a=\frac{15}{3\sqrt{2}}$$

Divide 15 by 3\sqrt{2}.

$$a=\frac{5\sqrt{2}}{2}$$