Solve px^2+30x+25=0

$$p x ^ { 2 } + 30 x + 25 = 0$$

Solve for p

$$p=-\frac{5\left(6x+5\right)}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 30x from both sides. Anything subtracted from zero gives its negation.

$$px^{2}+25=-30x$$

Subtract 25 from both sides.

$$px^{2}=-30x-25$$

The equation is in standard form.

$$x^{2}p=-30x-25$$

Divide both sides by x^{2}.

$$\frac{x^{2}p}{x^{2}}=\frac{-30x-25}{x^{2}}$$

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

$$p=\frac{-30x-25}{x^{2}}$$

Divide -30x-25 by x^{2}.

$$p=-\frac{5\left(6x+5\right)}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{5\left(\sqrt{9-p}-3\right)}{p}\text{; }x=-\frac{5\left(\sqrt{9-p}+3\right)}{p}\text{, }&p\neq 0\\x=-\frac{5}{6}\text{, }&p=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{5\left(\sqrt{9-p}-3\right)}{p}\text{; }x=-\frac{5\left(\sqrt{9-p}+3\right)}{p}\text{, }&p\neq 0\text{ and }p\leq 9\\x=-\frac{5}{6}\text{, }&p=0\end{matrix}\right.$$