Х^2 - 14х - 32 =0
5х^2 - 12х +7 =0
-2х^2 +х + 15 =0
4х^2 +х - 33 = 0

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To solve these quadratic equations, we can use the quadratic formula:

For the equation Х^2 - 14х - 32 = 0:
a = 1, b = -14, c = -32
Plugging these values into the quadratic formula:
x = (-(-14) ± sqrt((-14)^2 - 41(-32))) / (2*1)
x = (14 ± sqrt(196 + 128)) / 2
x = (14 ± sqrt(324)) / 2
x = (14 ± 18) / 2
This gives us two solutions: x1 = 16 and x2 = -2.

For the equation 5х^2 - 12х + 7 = 0:
a = 5, b = -12, c = 7
Plugging these values into the quadratic formula:
x = (12 ± sqrt((-12)^2 - 457)) / (2*5)
x = (12 ± sqrt(144 - 140)) / 10
x = (12 ± 2) / 10
This gives us two solutions: x1 = 1 and x2 = 7/5.

For the equation -2х^2 + х + 15 = 0:
a = -2, b = 1, c = 15
Plugging these values into the quadratic formula:
x = (-1 ± sqrt(1 - 4(-2)15)) / (2*(-2))
x = (-1 ± sqrt(1 + 120)) / -4
x = (-1 ± sqrt(121)) / -4
x = (-1 ± 11) / -4
This gives us two solutions: x1 = 3 and x2 = -5.

For the equation 4х^2 + х - 33 = 0:
a = 4, b = 1, c = -33
Plugging these values into the quadratic formula:
x = (-1 ± sqrt(1 + 4433)) / (2*4)
x = (-1 ± sqrt(1 + 528)) / 8
x = (-1 ± sqrt(529)) / 8
x = (-1 ± 23) / 8
This gives us two solutions: x1 = 3 and x2 = -11/4.