2x-(x+1) =3x²-6

Let's simplify the equation step by step.

Starting with the left side of the equation:

2x - (x + 1)

Use the distributive property to remove the parentheses:

2x - x - 1

Combine like terms:

x - 1

Now looking at the right side of the equation:

3x² - 6

The equation can now be written as:

x - 1 = 3x² - 6

To solve for x, we can set the equation equal to zero by subtracting x from both sides:

0 = 3x² - x - 5

Now, we have a quadratic equation in standard form. To solve this, we can either factor or use the quadratic formula.

If we attempt to factor, we need to find two numbers that multiply to give -15 (the product of the leading coefficient and the constant term) and add up to -1 (the coefficient of the linear term). However, there are no such pair of numbers. Therefore, we will use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 3, b = -1, and c = -5.

Substituting the values into the formula:

x = (1 ± √((-1)² - 4(3)(-5))) / (2(3))

Simplifying further:

x = (1 ± √(1 + 60)) / 6

x = (1 ± √61) / 6

Therefore, the two possible solutions for x are:

x = (1 + √61) / 6 x = (1 - √61) / 6