Solve x=frac{sqrt{3*3^2}+sqrt4*3^3}{2^2y-5}

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

Solve for y

$$y=\frac{5}{4}+\frac{27\sqrt{3}}{4x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to \frac{5}{4} since division by zero is not defined. Multiply both sides of the equation by 4y-5.

$$x\left(4y-5\right)=\sqrt{3\times 3^{2}}+\left(\sqrt{4\times 3}\right)^{3}$$

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

$$x\left(4y-5\right)=\sqrt{3^{3}}+\left(\sqrt{4\times 3}\right)^{3}$$

Use the distributive property to multiply x by 4y-5.

$$4xy-5x=\sqrt{3^{3}}+\left(\sqrt{4\times 3}\right)^{3}$$

Calculate 3 to the power of 3 and get 27.

$$4xy-5x=\sqrt{27}+\left(\sqrt{4\times 3}\right)^{3}$$

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}.

$$4xy-5x=3\sqrt{3}+\left(\sqrt{4\times 3}\right)^{3}$$

Multiply 4 and 3 to get 12.

$$4xy-5x=3\sqrt{3}+\left(\sqrt{12}\right)^{3}$$

Add 5x to both sides.

$$4xy=3\sqrt{3}+\left(\sqrt{12}\right)^{3}+5x$$

The equation is in standard form.

$$4xy=5x+\left(\sqrt{12}\right)^{3}+3\sqrt{3}$$

Divide both sides by 4x.

$$\frac{4xy}{4x}=\frac{5x+27\sqrt{3}}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$y=\frac{5x+27\sqrt{3}}{4x}$$

Divide 27\sqrt{3}+5x by 4x.

$$y=\frac{5}{4}+\frac{27\sqrt{3}}{4x}$$

Variable y cannot be equal to \frac{5}{4}.

$$y=\frac{5}{4}+\frac{27\sqrt{3}}{4x}\text{, }y\neq \frac{5}{4}$$

Solve for x

$$x=\frac{27\sqrt{3}}{4y-5}$$

$$y\neq \frac{5}{4}$$