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

1 Answer
Oct 25, 2015

Answer:

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)#