Question

Solve the following equation using the quadratic formula: 3x2−1=6x

Answer 1

Step by step explanation :

3x² - 1 = 6x

3x² - 6x - 1 = 0

Quadratic Formula

x = -b + or - √b² - 4ac

2a

Solution

a = 3

b = -6

c = -1

Substitute the given

x = -(-6) + or - √(6)² - 4(3)(-1)

2(3)

solution

x = 6 +or- √36+12

6

x = 6 +or - √48

6

x = 6 +or - 4√3

6

x = 6 - 4√3 or

6

x = 6 + 4√3

6

Simply the the expression by dividing it by two.

therefore

x = 3 - 2√3

3

or

x = 3 + 2√3

3

Answer : x = 3 - 2√3

3

or

x = 3 + 2√3

3

Answer 2

`\displaystyle{x=1\pm (2√(3))/(3)}`

Explanation:

We are given the equation below:

`\displaystyle{3x^2-1=6x}`

Rearrange in the term of quadratic expressions:

`\displaystyle{3x^2-6x-1=0}`

Apply the quadratic formula, which is:

`\displaystyle{x = (-b \pm √(b^2-4ac))/(2a)}`

Here, a = 3, b = -6 and c = -1. Therefore:

`\displaystyle{x = (-(-6) \pm √((-6)^2-4(3)(-1)))/(2(3))}\\\\\displaystyle{x = (6 \pm √(36+12))/(6)}\\\\\displaystyle{x = (6 \pm √(48))/(6)}\\\\\displaystyle{x = (6\pm 4√(3))/(6)}\\\\\displaystyle{x=1\pm (2√(3))/(3)}`

Therefore, the solutions are:

`\displaystyle{x=1\pm (2√(3))/(3)}`