Solve kr^2-14x-5=0

$$k r ^ { 2 } - 14 x - 5 = 0$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=\frac{14x+5}{r^{2}}\text{, }&r\neq 0\\k\in \mathrm{C}\text{, }&x=-\frac{5}{14}\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 14x to both sides. Anything plus zero gives itself.

$$kr^{2}-5=14x$$

Add 5 to both sides.

$$kr^{2}=14x+5$$

The equation is in standard form.

$$r^{2}k=14x+5$$

Divide both sides by r^{2}.

$$\frac{r^{2}k}{r^{2}}=\frac{14x+5}{r^{2}}$$

Dividing by r^{2} undoes the multiplication by r^{2}.

$$k=\frac{14x+5}{r^{2}}$$

Solve for k

$$\left\{\begin{matrix}k=\frac{14x+5}{r^{2}}\text{, }&r\neq 0\\k\in \mathrm{R}\text{, }&x=-\frac{5}{14}\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 14x to both sides. Anything plus zero gives itself.

$$kr^{2}-5=14x$$

Add 5 to both sides.

$$kr^{2}=14x+5$$

The equation is in standard form.

$$r^{2}k=14x+5$$

Divide both sides by r^{2}.

$$\frac{r^{2}k}{r^{2}}=\frac{14x+5}{r^{2}}$$

Dividing by r^{2} undoes the multiplication by r^{2}.

$$k=\frac{14x+5}{r^{2}}$$

Solve for r (complex solution)

$$\left\{\begin{matrix}r=-ik^{-\frac{1}{2}}\sqrt{-14x-5}\text{; }r=ik^{-\frac{1}{2}}\sqrt{-14x-5}\text{, }&k\neq 0\\r\in \mathrm{C}\text{, }&x=-\frac{5}{14}\text{ and }k=0\end{matrix}\right.$$

Solve for r

$$\left\{\begin{matrix}r=\sqrt{\frac{14x+5}{k}}\text{; }r=-\sqrt{\frac{14x+5}{k}}\text{, }&\left(x\geq -\frac{5}{14}\text{ and }k>0\right)\text{ or }\left(x\leq -\frac{5}{14}\text{ and }k<0\right)\\r\in \mathrm{R}\text{, }&x=-\frac{5}{14}\text{ and }k=0\end{matrix}\right.$$