Solve y_x^alpha-24x+16=0

$$y _ { x } ^ { \alpha } - 24 x + 16 = 0$$

Solve for x (complex solution)

$$x=\frac{y_{x}^{\alpha }+16}{24}$$

Steps for Solving Linear Equation

Subtract y_{x}^{\alpha } from both sides. Anything subtracted from zero gives its negation.

$$-24x+16=-y_{x}^{\alpha }$$

Subtract 16 from both sides.

$$-24x=-y_{x}^{\alpha }-16$$

Divide both sides by -24.

$$\frac{-24x}{-24}=\frac{-y_{x}^{\alpha }-16}{-24}$$

Dividing by -24 undoes the multiplication by -24.

$$x=\frac{-y_{x}^{\alpha }-16}{-24}$$

Divide -y_{x}^{\alpha }-16 by -24.

$$x=\frac{y_{x}^{\alpha }}{24}+\frac{2}{3}$$

Solve for x

$$x=\frac{y_{x}^{\alpha }+16}{24}$$

$$\left(y_{x}<0\text{ and }Denominator(\alpha )\text{bmod}2=1\right)\text{ or }\left(y_{x}=0\text{ and }\alpha >0\right)\text{ or }y_{x}>0$$

Steps for Solving Linear Equation

Subtract y_{x}^{\alpha } from both sides. Anything subtracted from zero gives its negation.

$$-24x+16=-y_{x}^{\alpha }$$

Subtract 16 from both sides.

$$-24x=-y_{x}^{\alpha }-16$$

Divide both sides by -24.

$$\frac{-24x}{-24}=\frac{-y_{x}^{\alpha }-16}{-24}$$

Dividing by -24 undoes the multiplication by -24.

$$x=\frac{-y_{x}^{\alpha }-16}{-24}$$

Divide -y_{x}^{\alpha }-16 by -24.

$$x=\frac{y_{x}^{\alpha }}{24}+\frac{2}{3}$$

Solve for y_x (complex solution)

$$y_{x}=e^{\frac{Im(\alpha )arg(-8\left(2-3x\right))+iRe(\alpha )arg(-8\left(2-3x\right))}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}-\frac{2iRe(\alpha )\pi n_{1}}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}-\frac{2\pi n_{1}Im(\alpha )}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}}\left(|8\left(2-3x\right)|\right)^{\frac{Re(\alpha )-iIm(\alpha )}{\left(Re(\alpha )\right)^{2}+\left(Im(\alpha )\right)^{2}}}$$

$$n_{1}\in \mathrm{Z}$$

Solve for y_x

$$\left\{\begin{matrix}y_{x}=\left(24x-16\right)^{\frac{1}{\alpha }}\text{, }&\left(Numerator(\alpha )\text{bmod}2=1\text{ and }Denominator(\alpha )\text{bmod}2=1\text{ and }x<\frac{2}{3}\text{ and }\left(24x-16\right)^{\frac{1}{\alpha }}\neq 0\right)\text{ or }\left(\left(24x-16\right)^{\frac{1}{\alpha }}<0\text{ and }x>\frac{2}{3}\text{ and }\alpha \neq 0\text{ and }Denominator(\alpha )\text{bmod}2=1\right)\text{ or }\left(\alpha >0\text{ and }x=\frac{2}{3}\right)\text{ or }\left(\left(24x-16\right)^{\frac{1}{\alpha }}>0\text{ and }x>\frac{2}{3}\text{ and }\alpha \neq 0\right)\\y_{x}=-\left(24x-16\right)^{\frac{1}{\alpha }}\text{, }&\left(x<\frac{2}{3}\text{ and }Numerator(\alpha )\text{bmod}2=1\text{ and }Numerator(\alpha )\text{bmod}2=0\text{ and }Denominator(\alpha )\text{bmod}2=1\text{ and }\left(24x-16\right)^{\frac{1}{\alpha }}\neq 0\right)\text{ or }\left(x>\frac{2}{3}\text{ and }\alpha \neq 0\text{ and }\left(24x-16\right)^{\frac{1}{\alpha }}>0\text{ and }Numerator(\alpha )\text{bmod}2=0\text{ and }Denominator(\alpha )\text{bmod}2=1\right)\text{ or }\left(Numerator(\alpha )\text{bmod}2=0\text{ and }x=\frac{2}{3}\text{ and }\alpha >0\right)\text{ or }\left(x>\frac{2}{3}\text{ and }\alpha \neq 0\text{ and }\left(24x-16\right)^{\frac{1}{\alpha }}<0\text{ and }Numerator(\alpha )\text{bmod}2=0\right)\\y_{x}\neq 0\text{, }&\alpha =0\text{ and }x=\frac{17}{24}\end{matrix}\right.$$