Find the Discriminant f(x)=ax^2+bx+c

$f (x) = a x^{2} + b x + c$

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

Subtract $b x$ from both sides of the equation.

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

Subtract $c$ from 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.

Simplify each term.

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.

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

Move the negative in front of the fraction.

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

Move the negative in front of the fraction.

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