Solve ax^2+dx+e=0

$$a x ^ { 2 } + d x + e = 0$$

Solve for a

$$a=-\frac{dx+e}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract dx from both sides. Anything subtracted from zero gives its negation.

$$ax^{2}+e=-dx$$

Subtract e from both sides.

$$ax^{2}=-dx-e$$

The equation is in standard form.

$$x^{2}a=-dx-e$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{-dx-e}{x^{2}}$$

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

$$a=\frac{-dx-e}{x^{2}}$$

Divide -dx-e by x^{2}.

$$a=-\frac{dx+e}{x^{2}}$$

Solve for d

$$d=-ax-\frac{e}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$dx+e=-ax^{2}$$

Subtract e from both sides.

$$dx=-ax^{2}-e$$

The equation is in standard form.

$$xd=-ax^{2}-e$$

Divide both sides by x.

$$\frac{xd}{x}=\frac{-ax^{2}-e}{x}$$

Dividing by x undoes the multiplication by x.

$$d=\frac{-ax^{2}-e}{x}$$

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

$$d=-ax-\frac{e}{x}$$