Question

When a number is added to six times its square, the result is twelve. Find the number.

Answer 1

Let's represent our number as x.
x is being added to 6 * x², and it equals 12

`x + 6x^(2)=12\\6x^(2)+x-12=0`
Factor:

`6x^(2)+x-12=0\\(2x+3)(3x-4)=0`
Solve for x:

`(2x+3)=0\\2x=-3\\x=(-3)/(2)\\\\(3x-4)=0\\3x=4\\x=(4)/(3)`

Therefore, x = -3/2 and 4/3.