Solve for a ax^2-bx-c=0 for a

$a x^{2} - b x - c = 0$ for $a$

Move all terms not containing $a$ to the right side of the equation.

Add $b x$ to both sides of the equation.

$a x^{2} - c = b x$

Add $c$ to both sides of the equation.

$a x^{2} = b x + c$

Divide each term in $a x^{2} = b x + c$ by $x^{2}$ and simplify.

Divide each term in $a x^{2} = b x + c$ by $x^{2}$ .

$\frac{a x^{2}}{x^{2}} = \frac{b x}{x^{2}} + \frac{c}{x^{2}}$

Simplify the left side.

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{a x^{2}}{x^{2}} = \frac{b x}{x^{2}} + \frac{c}{x^{2}}$

Divide $a$ by $1$ .

$a = \frac{b x}{x^{2}} + \frac{c}{x^{2}}$

Simplify the right side.

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $b x$ .

$a = \frac{x b}{x^{2}} + \frac{c}{x^{2}}$

Cancel the common factors.

Factor $x$ out of $x^{2}$ .

$a = \frac{x b}{x \cdot x} + \frac{c}{x^{2}}$

Cancel the common factor.

$a = \frac{x b}{x \cdot x} + \frac{c}{x^{2}}$

Rewrite the expression.

$a = \frac{b}{x} + \frac{c}{x^{2}}$