To solve the quadratic equation 12x^2 + 39x - 16 = 0, we can use the quadratic formula, which is given by:
x = (-b ±√(b^2 - 4ac))/(2a)
Here, a = 12, b = 39, and c = -16. Substituting these values into the formula, we get:
x = (-39 ±√(39^2 - 4 · 12 · (-16)))/(2 · 12)
Now, let's simplify the expression:
x = (-39 ±√(1521 + 768))/24
x = (-39 ±√2289)/24
x = (-39 ± 47.874)/24
Therefore, the solutions are:
x_1 = (-39 + 47.874)/24≈ 0.412
x_2 = (-39 - 47.874)/24≈ -2.029
So, the solutions to the equation 12x^2 + 39x - 16 = 0 are approximately x ≈ 0.412 and x ≈ -2.029.