Solve for n x^2-4nx+4m>0

$x^{2} - 4 n x + 4 m > 0$

Step 1

Move all terms not containing $n$ to the right side of the inequality.

Subtract $x^{2}$ from both sides of the inequality.

$- 4 n x + 4 m > - x^{2}$

Subtract $4 m$ from both sides of the inequality.

$- 4 n x > - x^{2} - 4 m$

Step 2

Divide each term in $- 4 n x > - x^{2} - 4 m$ by $- 4 x$ and simplify.

Divide each term in $- 4 n x > - x^{2} - 4 m$ by $- 4 x$ .

$\frac{- 4 n x}{- 4 x} > \frac{- x^{2}}{- 4 x} + \frac{- 4 m}{- 4 x}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 n x}{- 4 x} > \frac{- x^{2}}{- 4 x} + \frac{- 4 m}{- 4 x}$

Rewrite the expression.

$\frac{n x}{x} > \frac{- x^{2}}{- 4 x} + \frac{- 4 m}{- 4 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{n x}{x} > \frac{- x^{2}}{- 4 x} + \frac{- 4 m}{- 4 x}$

Divide $n$ by $1$ .

$n > \frac{- x^{2}}{- 4 x} + \frac{- 4 m}{- 4 x}$

Simplify the right side.

Simplify each term.

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

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

$n > \frac{x (- x)}{- 4 x} + \frac{- 4 m}{- 4 x}$

Cancel the common factors.

Factor $x$ out of $- 4 x$ .

$n > \frac{x (- x)}{x \cdot - 4} + \frac{- 4 m}{- 4 x}$

Cancel the common factor.

$n > \frac{x (- x)}{x \cdot - 4} + \frac{- 4 m}{- 4 x}$

Rewrite the expression.

$n > \frac{- x}{- 4} + \frac{- 4 m}{- 4 x}$

Dividing two negative values results in a positive value.

$n > \frac{x}{4} + \frac{- 4 m}{- 4 x}$

Cancel the common factor of $- 4$ .

Cancel the common factor.

$n > \frac{x}{4} + \frac{- 4 m}{- 4 x}$

Rewrite the expression.

$n > \frac{x}{4} + \frac{m}{x}$