Solve 2kx^2+6x+1=0

$$2 k x ^ { 2 } + 6 x + 1 = 0$$

Solve for k

$$k=-\frac{6x+1}{2x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 6x from both sides. Anything subtracted from zero gives its negation.

$$2kx^{2}+1=-6x$$

Subtract 1 from both sides.

$$2kx^{2}=-6x-1$$

The equation is in standard form.

$$2x^{2}k=-6x-1$$

Divide both sides by 2x^{2}.

$$\frac{2x^{2}k}{2x^{2}}=\frac{-6x-1}{2x^{2}}$$

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

$$k=\frac{-6x-1}{2x^{2}}$$

Divide -6x-1 by 2x^{2}.

$$k=-\frac{3x+\frac{1}{2}}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{9-2k}-3}{2k}\text{; }x=-\frac{\sqrt{9-2k}+3}{2k}\text{, }&k\neq 0\\x=-\frac{1}{6}\text{, }&k=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{9-2k}-3}{2k}\text{; }x=-\frac{\sqrt{9-2k}+3}{2k}\text{, }&k\neq 0\text{ and }k\leq \frac{9}{2}\\x=-\frac{1}{6}\text{, }&k=0\end{matrix}\right.$$