4a^2-15=17a

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Solution for 4a^2-15=17a equation:


Simplifying
4a2 + -15 = 17a

Reorder the terms:
-15 + 4a2 = 17a

Solving
-15 + 4a2 = 17a

Solving for variable 'a'.

Reorder the terms:
-15 + -17a + 4a2 = 17a + -17a

Combine like terms: 17a + -17a = 0
-15 + -17a + 4a2 = 0

Factor a trinomial.
(-3 + -4a)(5 + -1a) = 0

Subproblem 1

Set the factor '(-3 + -4a)' equal to zero and attempt to solve: Simplifying -3 + -4a = 0 Solving -3 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4a = 0 + 3 -4a = 0 + 3 Combine like terms: 0 + 3 = 3 -4a = 3 Divide each side by '-4'. a = -0.75 Simplifying a = -0.75

Subproblem 2

Set the factor '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5

Solution

a = {-0.75, 5}

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