Question

Using the quadratic formula to solve 5x = 6x^2 – 3, what are the values of x?

Answer 1

Correct Choice: Second Option

`\displaystyle x=(5\pm √(97))/(12)`

Explanation:

Standard Form of Quadratic Function

The standard representation of a quadratic function is:

`f(x)=ax^2+bx+c`

where a,b, and c are constants.

Solving with the quadratic formula:

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

We have the following equation to solve:

`5x = 6x^2 -3`

Rearranging all the terms to the left side:

`6x^2 -5x- 3=0`

Comparing with the general form of the quadratic equation: a=6, b=-5, c=-3. Apply the formula:

`\displaystyle x=(-(-5)\pm √((-5)^2-4(6)(-3)))/(2(6))`

`\displaystyle x=(5\pm √(25+72))/(12)`

`\boxed{\displaystyle x=(5\pm √(97))/(12)}`

Correct Choice: Second Option