Solve -6x^2+2ax-2a=-2

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

Solve for a

$$a=-\frac{1-3x^{2}}{x-1}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Add 6x^{2} to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 2x-2.

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

Dividing by 2x-2 undoes the multiplication by 2x-2.

$$a=\frac{6x^{2}-2}{2x-2}$$

Divide -2+6x^{2} by 2x-2.

$$a=\frac{3x^{2}-1}{x-1}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{a^{2}-12a+12}+a}{6}$$

$$x=\frac{\sqrt{a^{2}-12a+12}+a}{6}$$

Solve for x

$$x=\frac{-\sqrt{a^{2}-12a+12}+a}{6}$$

$$x=\frac{\sqrt{a^{2}-12a+12}+a}{6}\text{, }a\geq 2\sqrt{6}+6\text{ or }a\leq 6-2\sqrt{6}$$