Solve for x.
20x2 + 5x – 6 = 6x2 – 12x
(1 point)
a. x = three-halves, –two-sevenths
b. x = –three-halves, two-sevenths
c. x = 1, –three-sevenths
d. x = 1, three-sevenths
To solve the equation 20x^2 + 5x - 6 = 6x^2 - 12x, we need to combine like terms and set the equation equal to zero.
By subtracting 6x^2 and adding 12x on both sides, we get:
20x^2 + 5x - 6 - 6x^2 + 12x = 0
14x^2 + 17x - 6 = 0
Now, we can factor the quadratic equation:
(2x - 1)(7x + 6) = 0
Setting each factor equal to zero, we have two possible solutions:
2x - 1 = 0 --> 2x = 1 --> x = 1/2
7x + 6 = 0 --> 7x = -6 --> x = -6/7
Therefore, the solutions are x = 1/2 and x = -6/7.
The correct answer is:
a. x = three-halves, –two-sevenths