Solve rx^2+2x-24=0

$$r x ^ { 2 } + 2 x - 24 = 0$$

Solve for r

$$r=-\frac{2\left(x-12\right)}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$rx^{2}-24=-2x$$

Add 24 to both sides.

$$rx^{2}=-2x+24$$

The equation is in standard form.

$$x^{2}r=24-2x$$

Divide both sides by x^{2}.

$$\frac{x^{2}r}{x^{2}}=\frac{24-2x}{x^{2}}$$

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

$$r=\frac{24-2x}{x^{2}}$$

Divide -2x+24 by x^{2}.

$$r=\frac{2\left(12-x\right)}{x^{2}}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{24r+1}-1}{r}\text{; }x=-\frac{\sqrt{24r+1}+1}{r}\text{, }&r\neq 0\text{ and }r\geq -\frac{1}{24}\\x=12\text{, }&r=0\end{matrix}\right.$$