Solve ax^2-bx+3=0

$$a x ^ { 2 } - b x + 3 = 0$$

Solve for a

$$a=\frac{bx-3}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$ax^{2}+3=bx$$

Subtract 3 from both sides.

$$ax^{2}=bx-3$$

The equation is in standard form.

$$x^{2}a=bx-3$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{bx-3}{x^{2}}$$

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

$$a=\frac{bx-3}{x^{2}}$$

Solve for b

$$b=ax+\frac{3}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$-bx+3=-ax^{2}$$

Subtract 3 from both sides.

$$-bx=-ax^{2}-3$$

The equation is in standard form.

$$\left(-x\right)b=-ax^{2}-3$$

Divide both sides by -x.

$$\frac{\left(-x\right)b}{-x}=\frac{-ax^{2}-3}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$b=\frac{-ax^{2}-3}{-x}$$

Divide -ax^{2}-3 by -x.

$$b=ax+\frac{3}{x}$$