Solve AX^2+7X+6=0

$$A X ^ { 2 } + 7 X + 6 = 0$$

Solve for A

$$A=-\frac{7X+6}{X^{2}}$$

$$X\neq 0$$

Steps for Solving Linear Equation

Subtract 7X from both sides. Anything subtracted from zero gives its negation.

$$AX^{2}+6=-7X$$

Subtract 6 from both sides.

$$AX^{2}=-7X-6$$

The equation is in standard form.

$$X^{2}A=-7X-6$$

Divide both sides by X^{2}.

$$\frac{X^{2}A}{X^{2}}=\frac{-7X-6}{X^{2}}$$

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

$$A=\frac{-7X-6}{X^{2}}$$

Divide -7X-6 by X^{2}.

$$A=-\frac{7X+6}{X^{2}}$$

Solve for X

$$\left\{\begin{matrix}X=\frac{\sqrt{49-24A}-7}{2A}\text{; }X=-\frac{\sqrt{49-24A}+7}{2A}\text{, }&A\neq 0\text{ and }A\leq \frac{49}{24}\\X=-\frac{6}{7}\text{, }&A=0\end{matrix}\right.$$