Solve kx^2-19x+26=0

$$k x ^ { 2 } - 19 x + 26 = 0$$

Solve for k

$$k=-\frac{26-19x}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add 19x to both sides. Anything plus zero gives itself.

$$kx^{2}+26=19x$$

Subtract 26 from both sides.

$$kx^{2}=19x-26$$

The equation is in standard form.

$$x^{2}k=19x-26$$

Divide both sides by x^{2}.

$$\frac{x^{2}k}{x^{2}}=\frac{19x-26}{x^{2}}$$

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

$$k=\frac{19x-26}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{361-104k}+19}{2k}\text{; }x=\frac{-\sqrt{361-104k}+19}{2k}\text{, }&k\neq 0\\x=\frac{26}{19}\text{, }&k=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{361-104k}+19}{2k}\text{; }x=\frac{-\sqrt{361-104k}+19}{2k}\text{, }&k\neq 0\text{ and }k\leq \frac{361}{104}\\x=\frac{26}{19}\text{, }&k=0\end{matrix}\right.$$