Solve 23*-f(x)=sqrt{x^2-5x}

$$23 \cdot - f ( x ) = \sqrt { x ^ { 2 } - 5 x }$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{\sqrt{x\left(x-5\right)}}{23x}\text{, }&x\geq 5\text{ or }x<0\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 23 and -1 to get -23.

$$-23fx=\sqrt{x^{2}-5x}$$

The equation is in standard form.

$$\left(-23x\right)f=\sqrt{x^{2}-5x}$$

Divide both sides by -23x.

$$\frac{\left(-23x\right)f}{-23x}=\frac{\sqrt{x\left(x-5\right)}}{-23x}$$

Dividing by -23x undoes the multiplication by -23x.

$$f=\frac{\sqrt{x\left(x-5\right)}}{-23x}$$

Divide \sqrt{x\left(-5+x\right)} by -23x.

$$f=-\frac{\sqrt{x\left(x-5\right)}}{23x}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{5}{1-529f^{2}}\text{, }&f>\frac{1}{23}\text{ or }\left(f>-\frac{1}{23}\text{ and }f\leq 0\right)\end{matrix}\right.$$