First, put the equation in standard form:
6x^2 + color(6x) - 36 = -6x + color(6x)
6x^2 + 6x - 36 = 0
We can now use the quadratic equation to solve this problem:
The quadratic formula states:
For color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0, the values of x which are the solutions to the equation are given by:
x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))
Substituting:
color(red)(6) for color(red)(a)
color(blue)(6) for color(blue)(b)
color(green)(-36) for color(green)(c) gives:
x = (-color(blue)(6) +- sqrt(color(blue)(6)^2 - (4 * color(red)(6) * color(green)(-36))))/(2 * color(red)(6))
x = (-color(blue)(6) +- sqrt(36 - (-864)))/12
x = (-color(blue)(6) +- sqrt(36 + 864))/12
x = (-color(blue)(6) - sqrt(900))/12 and x = (-color(blue)(6) + sqrt(900))/12
x = (-color(blue)(6) - 30)/12 and x = (-color(blue)(6) + 30)/12
x = -36/12 and x = 24/12
x = -3 and x = 2
Another way of solving this quadratic equation:
6x^2+6x-36=0
(3x+9)(2x-4)=0
3x must be -9 or 2x must be 4 to end up with 0.
3x=-9
x=-3
2x=4
x=2
Therefor x=-3 or x=2