Solve 7*y=sqrt{3x/5+5/sqrt[3]{x}}-8sqrt[3]{x^5}+4/9

$$7 \cdot y = \sqrt { \frac { 3 x } { 5 } + \frac { 5 } { \sqrt[ 3 ] { x } } } - 8 \sqrt[ 3 ] { x ^ { 5 } } + \frac { 4 } { 9 }$$

Solve for y (complex solution)

$$y=-\frac{8x^{\frac{5}{3}}}{7}+\frac{\sqrt{15x+125x^{-\frac{1}{3}}}}{35}+\frac{4}{63}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply -1 and 8 to get -8.

$$7y=\sqrt{\frac{3x}{5}+\frac{5}{\sqrt[3]{x}}}-8\sqrt[3]{x^{5}}+\frac{4}{9}$$

The equation is in standard form.

$$7y=-8\sqrt[3]{x^{5}}+\sqrt{\frac{3x}{5}+\frac{5}{\sqrt[3]{x}}}+\frac{4}{9}$$

Divide both sides by 7.

$$\frac{7y}{7}=\frac{-8x^{\frac{5}{3}}+\frac{\sqrt{15x+125x^{-\frac{1}{3}}}}{5}+\frac{4}{9}}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$y=\frac{-8x^{\frac{5}{3}}+\frac{\sqrt{15x+125x^{-\frac{1}{3}}}}{5}+\frac{4}{9}}{7}$$

Divide \frac{\sqrt{15x+125x^{-\frac{1}{3}}}}{5}-8x^{\frac{5}{3}}+\frac{4}{9} by 7.

$$y=-\frac{8x^{\frac{5}{3}}}{7}+\frac{\sqrt{15x+125x^{-\frac{1}{3}}}}{35}+\frac{4}{63}$$

Solve for y

$$y=-\frac{8x^{\frac{5}{3}}}{7}+\frac{\sqrt{15x^{\frac{4}{3}}+125}}{35\sqrt[6]{x}}+\frac{4}{63}$$

$$x>0$$

Steps for Solving Linear Equation

Multiply -1 and 8 to get -8.

$$7y=\sqrt{\frac{3x}{5}+\frac{5}{\sqrt[3]{x}}}-8\sqrt[3]{x^{5}}+\frac{4}{9}$$

The equation is in standard form.

$$7y=-8\sqrt[3]{x^{5}}+\sqrt{\frac{3x}{5}+\frac{5}{\sqrt[3]{x}}}+\frac{4}{9}$$

Divide both sides by 7.

$$\frac{7y}{7}=\frac{-8x^{\frac{5}{3}}+\frac{\sqrt{15x^{\frac{4}{3}}+125}}{5\sqrt[6]{x}}+\frac{4}{9}}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$y=\frac{-8x^{\frac{5}{3}}+\frac{\sqrt{15x^{\frac{4}{3}}+125}}{5\sqrt[6]{x}}+\frac{4}{9}}{7}$$

Divide \frac{4}{9}-8x^{\frac{5}{3}}+\frac{\sqrt{15x^{\frac{4}{3}}+125}}{5\sqrt[6]{x}} by 7.

$$y=-\frac{8x^{\frac{5}{3}}}{7}+\frac{\sqrt{15x^{\frac{4}{3}}+125}}{35\sqrt[6]{x}}+\frac{4}{63}$$