Question

How do you solve `2x^2=6x-2` using the quadratic formula?

Answer 1

`x=(3+sqrt(5))/2` or `(3-sqrt(5))/2`

Explanation:

Using quadratic formula, solution of the equation `ax^2+bx+c=0` is given by `x=(-b+-sqrt(b^2-4ac))/(2a)`. Note that the quadratic equation is in its general form.

Hence converting the equation to its general form, the equation `2x^2=6x−2` this becomes `2x^2-6x+2=0` or dividing by `2`, `x^2-3x+1=0` and as such `a=1, b=-3` and `c=1`.

Hence, solution is given by `x=(-(-3)+-sqrt((-3)^2-4*1*1))/(2*1)` or

`x=(3+-sqrt(9-4))/2` or `x=(3+-sqrt(5))/2` i.e.

`x=(3+sqrt(5))/2` or `(3-sqrt(5))/2`