Solve 1/2a*(sqrt{8}+sqrt{3})*sqrt{3}=300

$$\frac { 1 } { 2 } a \cdot ( \sqrt { 8 } + \sqrt { 3 } ) \cdot \sqrt { 3 } = 300$$

Solve for a

$$a=80\sqrt{6}-120\approx 75.959179423$$

Steps for Solving Linear Equation

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{1}{2}a\left(2\sqrt{2}+\sqrt{3}\right)\sqrt{3}=300$$

Use the distributive property to multiply \frac{1}{2}a by 2\sqrt{2}+\sqrt{3}.

$$\left(\frac{1}{2}a\times 2\sqrt{2}+\frac{1}{2}a\sqrt{3}\right)\sqrt{3}=300$$

Cancel out 2 and 2.

$$\left(a\sqrt{2}+\frac{1}{2}a\sqrt{3}\right)\sqrt{3}=300$$

Use the distributive property to multiply a\sqrt{2}+\frac{1}{2}a\sqrt{3} by \sqrt{3}.

$$a\sqrt{2}\sqrt{3}+\frac{1}{2}a\sqrt{3}\sqrt{3}=300$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$a\sqrt{2}\sqrt{3}+\frac{1}{2}a\times 3=300$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$a\sqrt{6}+\frac{1}{2}a\times 3=300$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$a\sqrt{6}+\frac{3}{2}a=300$$

Combine all terms containing a.

$$\left(\sqrt{6}+\frac{3}{2}\right)a=300$$

Divide both sides by \sqrt{6}+\frac{3}{2}.

$$\frac{\left(\sqrt{6}+\frac{3}{2}\right)a}{\sqrt{6}+\frac{3}{2}}=\frac{300}{\sqrt{6}+\frac{3}{2}}$$

Dividing by \sqrt{6}+\frac{3}{2} undoes the multiplication by \sqrt{6}+\frac{3}{2}.

$$a=\frac{300}{\sqrt{6}+\frac{3}{2}}$$

Divide 300 by \sqrt{6}+\frac{3}{2}.

$$a=80\sqrt{6}-120$$