Solve x^2+ax^2-5x-6=0

$$x ^ { 2 } + a x ^ { 2 } - 5 x - 6 = 0$$

Solve for a

$$a=-\frac{\left(x-6\right)\left(x+1\right)}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$ax^{2}-5x-6=-x^{2}$$

Add 5x to both sides.

$$ax^{2}-6=-x^{2}+5x$$

Add 6 to both sides.

$$ax^{2}=-x^{2}+5x+6$$

The equation is in standard form.

$$x^{2}a=6+5x-x^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=-\frac{\left(x-6\right)\left(x+1\right)}{x^{2}}$$

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

$$a=-\frac{\left(x-6\right)\left(x+1\right)}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{24a+49}+5}{2\left(a+1\right)}\text{; }x=\frac{-\sqrt{24a+49}+5}{2\left(a+1\right)}\text{, }&a\neq -1\\x=-\frac{6}{5}\text{, }&a=-1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{24a+49}+5}{2\left(a+1\right)}\text{; }x=\frac{-\sqrt{24a+49}+5}{2\left(a+1\right)}\text{, }&a\neq -1\text{ and }a\geq -\frac{49}{24}\\x=-\frac{6}{5}\text{, }&a=-1\end{matrix}\right.$$