Question

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

Answer 1

Answer:

Correct Choice: Second Option

$\displaystyle x=\frac{5\pm \sqrt{97}}{12}$

Step-by-step 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:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

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:

$\displaystyle x=\frac{-(-5)\pm \sqrt{(-5)^2-4(6)(-3)}}{2(6)}$

$\displaystyle x=\frac{5\pm \sqrt{25+72}}{12}$

$\boxed{\displaystyle x=\frac{5\pm \sqrt{97}}{12}}$

Correct Choice: Second Option