It is usually nicer to work with positive numbers, so add the opposite of the left side of the equation.
0 = 6y² + 9y -1
You identify a=6, b=9, c=-1 for the quadratic formula, which tells you
y = (-b ±√(b²-4ac))/(2a)
y = (-9 ±√(9²-4(6)(-1)))/(2·6)
y = (-9 ±√105)/12
y = -1.60, 0.10
The appropriate choice is
D, -1.6, 0.1
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You don't really need to solve the equation if you can test the offered solutions. Dividing by the coefficient of y², your equation becomes
y² + (3/2)y - (1/6) = 0
This tells you the sum of the roots will be -3/2 (the opposite of the y coefficient), and their product will be -1/6 (the constant term). Selections A and C have the wrong product; selection B has the wrong sum.