6x^2=5x+50

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Solution for 6x^2=5x+50 equation:


Simplifying
6x2 = 5x + 50

Reorder the terms:
6x2 = 50 + 5x

Solving
6x2 = 50 + 5x

Solving for variable 'x'.

Reorder the terms:
-50 + -5x + 6x2 = 50 + 5x + -50 + -5x

Reorder the terms:
-50 + -5x + 6x2 = 50 + -50 + 5x + -5x

Combine like terms: 50 + -50 = 0
-50 + -5x + 6x2 = 0 + 5x + -5x
-50 + -5x + 6x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-50 + -5x + 6x2 = 0

Factor a trinomial.
(-5 + -2x)(10 + -3x) = 0

Subproblem 1

Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5

Subproblem 2

Set the factor '(10 + -3x)' equal to zero and attempt to solve: Simplifying 10 + -3x = 0 Solving 10 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3x = 0 + -10 -3x = 0 + -10 Combine like terms: 0 + -10 = -10 -3x = -10 Divide each side by '-3'. x = 3.333333333 Simplifying x = 3.333333333

Solution

x = {-2.5, 3.333333333}

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