Solve x=frac{sqrt{3*3^2}+sqrt{4*3}}{2*3-5}

$$x = \frac{ \sqrt{ 3 \times { 3 }^{ 2 } } + \sqrt{ 4 \times 3 } }{ 2 \cdot 3-5 }$$

Solve for x

$$x=5\sqrt{3}\approx 8.660254038$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x=\frac{\sqrt{3^{3}}+\sqrt{4\times 3}}{2\times 3-5}$$

Calculate 3 to the power of 3 and get 27.

$$x=\frac{\sqrt{27}+\sqrt{4\times 3}}{2\times 3-5}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$x=\frac{3\sqrt{3}+\sqrt{4\times 3}}{2\times 3-5}$$

Multiply 4 and 3 to get 12.

$$x=\frac{3\sqrt{3}+\sqrt{12}}{2\times 3-5}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$x=\frac{3\sqrt{3}+2\sqrt{3}}{2\times 3-5}$$

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

$$x=\frac{5\sqrt{3}}{2\times 3-5}$$

Multiply 2 and 3 to get 6.

$$x=\frac{5\sqrt{3}}{6-5}$$

Subtract 5 from 6 to get 1.

$$x=\frac{5\sqrt{3}}{1}$$

Anything divided by one gives itself.

$$x=5\sqrt{3}$$

Assign x

$$x≔5\sqrt{3}$$