Solve ax^2+6x-1=0

$$a x ^ { 2 } + 6 x - 1 = 0$$

Solve for a

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

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

Add 1 to both sides.

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

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Solve for x (complex solution)

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

Solve for x

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