Solve 2x^2-(3-6a)x-2=0

$$2 x ^ { 2 } - ( 3 - 6 a ) x - 2 = 0$$

Solve for a

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

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3-6a by x.

$$2x^{2}-\left(3x-6ax\right)-2=0$$

To find the opposite of 3x-6ax, find the opposite of each term.

$$2x^{2}-3x+6ax-2=0$$

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

$$-3x+6ax-2=-2x^{2}$$

Add 3x to both sides.

$$6ax-2=-2x^{2}+3x$$

Add 2 to both sides.

$$6ax=-2x^{2}+3x+2$$

The equation is in standard form.

$$6xa=2+3x-2x^{2}$$

Divide both sides by 6x.

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

Dividing by 6x undoes the multiplication by 6x.

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

Divide \left(1+2x\right)\left(2-x\right) by 6x.

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

Solve for x

$$x=\frac{\sqrt{36a^{2}-36a+25}}{4}-\frac{3a}{2}+\frac{3}{4}$$

$$x=-\frac{\sqrt{36a^{2}-36a+25}}{4}-\frac{3a}{2}+\frac{3}{4}$$