Question

What is the quadratic equation of `3x^2 + 6x = 12`?

Answer 1

This is already a quadratic equation.

In standard form you might write it `3x^2+6x-12 = 0`

Explanation:

Standard form for a quadratic equation in one variable `x` is:

`ax^2+bx+c = 0`

In our case, we can get our equation into standard form by subtracting `12` from both sides to get:

`3x^2+6x-12 = 0`

In addition, all of the coefficients are divisible by `3`, so we can divide through by `3` to get the equivalent equation:

`x^2+2x-4 = 0`

...which is in standard form with `a=1`, `b=2` and `c = -4`.

Then we can use the quadratic formula to find the solutions:

`x = (-b +-sqrt(b^2-4ac))/(2a) = (2 +-sqrt(2^2-(4xx1xx-4)))/(2*1) = (2+-sqrt(4+16))/2`

`= (2+-sqrt(20))/2 = (2+-sqrt(2^2*5))/2 = (2+-sqrt(2^2)sqrt(5))/2 = (2+-2sqrt(5))/2`

`= 1+-sqrt(5)`