Final answer:
To solve the equation 6x²+17x = -12, use the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / (2a). Substituting the values of a, b, and c, we find two possible values for x: x = -2 or x = -3/2.
Step-by-step explanation:
To solve for the variable x in the equation 6x²+17x = -12, we need to bring all terms to one side and set the equation equal to zero. This gives us 6x² + 17x + 12 = 0. Now, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
where a = 6, b = 17, and c = 12. Plugging in these values, we get x = (-17 ± sqrt(17^2 - 4*6*12)) / (2*6). Simplifying further, we get x = (-17 ± sqrt(289 - 288)) / 12. This reduces to x = (-17 ± sqrt(1)) / 12. Finally, x = (-17 ± 1) / 12, which gives us two possible values for x: x = -2 or x = -rac{6}{2}.