Solve y=sqrt{200+600x/20+8^6}

$$y = \sqrt { \frac { 200 + 600 x } { 20 } + 8 ^ { 6 } }$$

Solve for x

$$x=\frac{y^{2}-262154}{30}$$

$$y\geq 0$$

Steps for Solving Radical Equations

Calculate 8 to the power of 6 and get 262144.

$$y=\sqrt{\frac{200+600x}{20}+262144}$$

Divide each term of 200+600x by 20 to get 10+30x.

$$y=\sqrt{10+30x+262144}$$

Add 10 and 262144 to get 262154.

$$y=\sqrt{262154+30x}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{262154+30x}=y$$

Square both sides of the equation.

$$30x+262154=y^{2}$$

Subtract 262154 from both sides of the equation.

$$30x+262154-262154=y^{2}-262154$$

Subtracting 262154 from itself leaves 0.

$$30x=y^{2}-262154$$

Divide both sides by 30.

$$\frac{30x}{30}=\frac{y^{2}-262154}{30}$$

Dividing by 30 undoes the multiplication by 30.

$$x=\frac{y^{2}-262154}{30}$$

Divide y^{2}-262154 by 30.

$$x=\frac{y^{2}}{30}-\frac{131077}{15}$$

Solve for x (complex solution)

$$x=\frac{y^{2}-262154}{30}$$

$$arg(y)<\pi \text{ or }y=0$$

Solve for y (complex solution)

$$y=\sqrt{30x+262154}$$

Solve for y

$$y=\sqrt{30x+262154}$$

$$x\geq -\frac{131077}{15}$$