x^2 - 15x + 16 = 0
That would factor nicely if it was x^2 - 15x - 16 = 0, but x^2 - 15x + 16 = 0 doesn't factor nicely.
Quadratic formula
x^2 - 15x + 16 = 0
x = (15 +- sqrt((-15)^2 - 4(1)(16))) / 2(1)
x = (15 +- sqrt(225 - 64)) / 2
x = (15 +- sqrt(161))/2
sqrt(161) doesn't factor, so the answer is:
x = (15 + sqrt(161))/2, (15 - sqrt(161))/2
.
3x^2 + 3x = 8
3x^2 + 3x - 8 = 0
(3x )(x ) = 0
That looks like it might not factor nicely, so. . . quadratic.
x = (-3 +- sqrt(3^2 - 4(3)(-8))) / 2(3)
x = (-3 +- sqrt(9 + 96)) / 6
x = (-3 +- sqrt(105))/6
Sqrt(105) doesn't facto, so the answer is:
x = (-3 + sqrt(105))/6, x = (-3 - sqrt(105))/6
.
7x^2 + x - 6 = 0
(7x )(x ) = 0
(7x - 6)(x + 1) = 0
7x - 6 = 0
7x = 6
x = 6/7
x + 1 = 0
x = -1
x = -1, x = 6/7