There are two ways, factoring or using the quadratic formula.
To factor, split the linear coefficient into m+n as follows:
m + n = -54 ; mn = (9)(-19) = -171
We can see that m = 3, n = -57.
9x2 – 54x – 19 = 0
9x2 + 3x - 57x - 19 = 0
3x(3x + 1) - 19(3x + 1) = 0
(3x - 19)(3x + 1) = 0
x = 19/3 or x = -1/3.
Or if you want to use the quadratic formula, x = [-b±√(b2 - 4ac)]/(2a), then:
x = [54 ± √((-54)2 - 4(9)(-19))]/[2(9)]
= [54 ± √(2916 + 684)]/18
= (54 ± √3600)/18
= (54 ± 60)/18
= (9 ± 10)/3
= 19/3 or -1/3
