83=5x^2+5x-17

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Solution for 83=5x^2+5x-17 equation:


Simplifying
83 = 5x2 + 5x + -17

Reorder the terms:
83 = -17 + 5x + 5x2

Solving
83 = -17 + 5x + 5x2

Solving for variable 'x'.

Combine like terms: 83 + 17 = 100
100 + -5x + -5x2 = -17 + 5x + 5x2 + 17 + -5x + -5x2

Reorder the terms:
100 + -5x + -5x2 = -17 + 17 + 5x + -5x + 5x2 + -5x2

Combine like terms: -17 + 17 = 0
100 + -5x + -5x2 = 0 + 5x + -5x + 5x2 + -5x2
100 + -5x + -5x2 = 5x + -5x + 5x2 + -5x2

Combine like terms: 5x + -5x = 0
100 + -5x + -5x2 = 0 + 5x2 + -5x2
100 + -5x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
100 + -5x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(20 + -1x + -1x2) = 0

Factor a trinomial.
5((4 + -1x)(5 + x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {4, -5}

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