Solve Ax^2+5x+2=0

$$A x ^ { 2 } + 5 x + 2 = 0$$

Solve for A

$$A=-\frac{5x+2}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 5x from both sides. Anything subtracted from zero gives its negation.

$$Ax^{2}+2=-5x$$

Subtract 2 from both sides.

$$Ax^{2}=-5x-2$$

The equation is in standard form.

$$x^{2}A=-5x-2$$

Divide both sides by x^{2}.

$$\frac{x^{2}A}{x^{2}}=\frac{-5x-2}{x^{2}}$$

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

$$A=\frac{-5x-2}{x^{2}}$$

Divide -5x-2 by x^{2}.

$$A=-\frac{5x+2}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{25-8A}-5}{2A}\text{; }x=-\frac{\sqrt{25-8A}+5}{2A}\text{, }&A\neq 0\\x=-\frac{2}{5}\text{, }&A=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{25-8A}-5}{2A}\text{; }x=-\frac{\sqrt{25-8A}+5}{2A}\text{, }&A\neq 0\text{ and }A\leq \frac{25}{8}\\x=-\frac{2}{5}\text{, }&A=0\end{matrix}\right.$$