Solve 2x^2-3px+5q=0

$$2 x ^ { 2 } - 3 p x + 5 q = 0$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{2x}{3}+\frac{5q}{3x}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&q=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-3px+5q=-2x^{2}$$

Subtract 5q from both sides.

$$-3px=-2x^{2}-5q$$

The equation is in standard form.

$$\left(-3x\right)p=-2x^{2}-5q$$

Divide both sides by -3x.

$$\frac{\left(-3x\right)p}{-3x}=\frac{-2x^{2}-5q}{-3x}$$

Dividing by -3x undoes the multiplication by -3x.

$$p=\frac{-2x^{2}-5q}{-3x}$$

Divide -2x^{2}-5q by -3x.

$$p=\frac{2x}{3}+\frac{5q}{3x}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{2x}{3}+\frac{5q}{3x}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&q=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-3px+5q=-2x^{2}$$

Subtract 5q from both sides.

$$-3px=-2x^{2}-5q$$

The equation is in standard form.

$$\left(-3x\right)p=-2x^{2}-5q$$

Divide both sides by -3x.

$$\frac{\left(-3x\right)p}{-3x}=\frac{-2x^{2}-5q}{-3x}$$

Dividing by -3x undoes the multiplication by -3x.

$$p=\frac{-2x^{2}-5q}{-3x}$$

Divide -2x^{2}-5q by -3x.

$$p=\frac{2x}{3}+\frac{5q}{3x}$$

Solve for q

$$q=-\frac{x\left(2x-3p\right)}{5}$$

Steps for Solving Linear Equation

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

$$-3px+5q=-2x^{2}$$

Add 3px to both sides.

$$5q=-2x^{2}+3px$$

The equation is in standard form.

$$5q=3px-2x^{2}$$

Divide both sides by 5.

$$\frac{5q}{5}=\frac{x\left(3p-2x\right)}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$q=\frac{x\left(3p-2x\right)}{5}$$