X²+7x-60=0 m²+m-90=0 2x²+x+2=0 x²+5x-6=0 (x+3)(x-4)=-12

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The given equations are:

1) x² + 7x - 60 =
2) m² + m - 90 =
3) 2x² + x + 2 =
4) x² + 5x - 6 =
5) (x+3)(x-4) = -12

To solve these equations, we can use the quadratic formula. The quadratic formula is given by:

For a quadratic equation of the form ax² + bx + c = 0, the solutions are given by:

x = (-b ± √(b² - 4ac)) / 2a

Let's solve the equations one by one:

1) x² + 7x - 60 = 0

a = 1, b = 7, c = -60

x = (-7 ± √(7² - 41(-60))) / 2*
x = (-7 ± √(49 + 240)) /
x = (-7 ± √289) /
x = (-7 ± 17) / 2

Two possible solutions
x = (-7 + 17) / 2 =
x = (-7 - 17) / 2 = -12

2) m² + m - 90 = 0

a = 1, b = 1, c = -90

m = (-1 ± √(1² - 41(-90))) / 2*
m = (-1 ± √(1 + 360)) /
m = (-1 ± √361) /
m = (-1 ± 19) / 2

Two possible solutions
m = (-1 + 19) / 2 =
m = (-1 - 19) / 2 = -10

3) 2x² + x + 2 = 0

a = 2, b = 1, c = 2

x = (-1 ± √(1² - 422)) / 2*
x = (-1 ± √(1 - 16)) /
x = (-1 ± √(-15)) /
x = (-1 ± i√15) / 4

Two possible solutions
x = (-1 + i√15) /
x = (-1 - i√15) / 4

4) x² + 5x - 6 = 0

a = 1, b = 5, c = -6

x = (-5 ± √(5² - 41(-6))) / 2*
x = (-5 ± √(25 + 24)) /
x = (-5 ± √49) /
x = (-5 ± 7) / 2

Two possible solutions
x = (-5 + 7) / 2 =
x = (-5 - 7) / 2 = -6

5) (x+3)(x-4) = -12

Expanding the left side
x² - 4x + 3x - 12 = -1
x² - x - 12 = -1
x² - x = 0

x(x - 1) = 0

Two possible solutions
x =
x = 1

These are the solutions to the given equations.