0=8x^2-620x+12000

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Solution for 0=8x^2-620x+12000 equation:


Simplifying
0 = 8x2 + -620x + 12000

Reorder the terms:
0 = 12000 + -620x + 8x2

Solving
0 = 12000 + -620x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + -12000 = -12000
-12000 + 620x + -8x2 = 12000 + -620x + 8x2 + -12000 + 620x + -8x2

Reorder the terms:
-12000 + 620x + -8x2 = 12000 + -12000 + -620x + 620x + 8x2 + -8x2

Combine like terms: 12000 + -12000 = 0
-12000 + 620x + -8x2 = 0 + -620x + 620x + 8x2 + -8x2
-12000 + 620x + -8x2 = -620x + 620x + 8x2 + -8x2

Combine like terms: -620x + 620x = 0
-12000 + 620x + -8x2 = 0 + 8x2 + -8x2
-12000 + 620x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-12000 + 620x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3000 + 155x + -2x2) = 0

Factor a trinomial.
4((-40 + x)(75 + -2x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-40 + x)' equal to zero and attempt to solve: Simplifying -40 + x = 0 Solving -40 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 0 + 40 Combine like terms: -40 + 40 = 0 0 + x = 0 + 40 x = 0 + 40 Combine like terms: 0 + 40 = 40 x = 40 Simplifying x = 40

Subproblem 2

Set the factor '(75 + -2x)' equal to zero and attempt to solve: Simplifying 75 + -2x = 0 Solving 75 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + -2x = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -2x = 0 + -75 -2x = 0 + -75 Combine like terms: 0 + -75 = -75 -2x = -75 Divide each side by '-2'. x = 37.5 Simplifying x = 37.5

Solution

x = {40, 37.5}

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