Х^2+3x+2=0 -x^2-2x+24=0 x^2-7x+12=0 -x^2-5x+6=0

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

For the equation x^2 + 3x + 2 = 0:
a = 1, b = 3, c = 2
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-3 ± √(3^2 - 412)) / 2*1
x = (-3 ± √(9 - 8)) / 2
x = (-3 ± √1) / 2
x = (-3 ± 1) / 2
x1 = (-3 + 1) / 2
x1 = -2 / 2
x1 = -1

x2 = (-3 - 1) / 2
x2 = -4 / 2
x2 = -2

So the solutions are x = -1 and x = -2.

For the equation -x^2 - 2x + 24 = 0:
a = -1, b = -2, c = 24
x = (-(-2) ± √((-2)^2 - 4(-1)24)) / 2*(-1)
x = (2 ± √(4 + 96)) / -2
x = (2 ± √100) / -2
x = (2 ± 10) / -2
x1 = (2 + 10) / -2
x1 = 12 / -2
x1 = -6

x2 = (2 - 10) / -2
x2 = -8 / -2
x2 = 4

So the solutions are x = -6 and x = 4.

For the equation x^2 - 7x + 12 = 0:
a = 1, b = -7, c = 12
x = (7 ± √((-7)^2 - 4112)) / 2*1
x = (7 ± √(49 - 48)) / 2
x = (7 ± √1) / 2
x = (7 ± 1) / 2
x1 = (7 + 1) / 2
x1 = 8 / 2
x1 = 4

x2 = (7 - 1) / 2
x2 = 6 / 2
x2 = 3

So the solutions are x = 4 and x = 3.

For the equation -x^2 - 5x + 6 = 0:
a = -1, b = -5, c = 6
x = (-(-5) ± √((-5)^2 - 4(-1)6)) / 2*(-1)
x = (5 ± √(25 + 24)) / -2
x = (5 ± √49) / -2
x = (5 ± 7) / -2
x1 = (5 + 7) / -2
x1 = 12 / -2
x1 = -6

x2 = (5 - 7) / -2
x2 = -2 / -2
x2 = 1

So the solutions are x = -6 and x = 1.