Solve Mx^2-nx+1=0

$$M x ^ { 2 } - n x + 1 = 0$$

Solve for M

$$M=\frac{nx-1}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Add nx to both sides. Anything plus zero gives itself.

$$Mx^{2}+1=nx$$

Subtract 1 from both sides.

$$Mx^{2}=nx-1$$

The equation is in standard form.

$$x^{2}M=nx-1$$

Divide both sides by x^{2}.

$$\frac{x^{2}M}{x^{2}}=\frac{nx-1}{x^{2}}$$

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

$$M=\frac{nx-1}{x^{2}}$$

Solve for n

$$n=Mx+\frac{1}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract Mx^{2} from both sides. Anything subtracted from zero gives its negation.

$$-nx+1=-Mx^{2}$$

Subtract 1 from both sides.

$$-nx=-Mx^{2}-1$$

The equation is in standard form.

$$\left(-x\right)n=-Mx^{2}-1$$

Divide both sides by -x.

$$\frac{\left(-x\right)n}{-x}=\frac{-Mx^{2}-1}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$n=\frac{-Mx^{2}-1}{-x}$$

Divide -Mx^{2}-1 by -x.

$$n=Mx+\frac{1}{x}$$