Find the solution to the equation below.
2x^2+3x-20=0

  x = -4, 5/2

Step-by-step explanation:

A quadratic can be solved may ways, including graphing, factoring, and the quadratic formula. You can also check possible answers by making use of the relationships between solutions and the coefficients.

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A graph is attached. It shows the solutions to be -4 and 5/2.

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When factored, the equation becomes ...

  (2x -5)(x +4) = 0 . . . . . has solutions x=-4, x=5/2 (these make the factors zero)

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Using the quadratic formula, the solutions of ax^2 +bx +c = 0 are found from ...

  x = (-b±√(b²-4ac))/(2a)

  x = (-3±√(3²-4(2)(-20))/(2(2)) = (-3±√169)/4 = {-16, +10}/4

  x = {-4, 5/2}

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For ax^2 +bx +c = 0, the solutions must satisfy ...

  product of solutions is c/a = -20/2 = -10

Only the first and last choices have this product.

  sum of solutions is -b/a = -3/2

Only the first choice (-4, 5/2) has this sum.

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

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step-by-step explanation: