Question

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

Answer 1

Answer: x = -3/2 and 4/3

Answer 2

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:
$(2x+3)=0\\2x=-3\\x=\frac{-3}{2}\\\\(3x-4)=0\\3x=4\\x=\frac{4}{3}$

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