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Question
Solve the quadratic equation:
`4sqrt(5)x^2 + 7x - 3sqrt(5) = 0`.
Solution
The given equation is
`4sqrt(5)x^2 + 7x - 3sqrt(5)`= 0.
⇒ `4sqrt(5)x^2 + 12x - 5x - 3sqrt(5)` = 0
⇒ `4x(sqrt(5)x + 3) - sqrt(5) (sqrt(5)x + 3)` = 0
⇒ `(sqrt(5)x + 3) (4x - sqrt(5))` = 0
⇒ `sqrt(5)x + 3 = 0 or 4x - sqrt(5)` = 0
⇒ `sqrt(5)x = -3 and 4x = sqrt(5)`
⇒ x = `-(3)/sqrt(5) and x = sqrt(5)/(4)`
so x = `-(3)/sqrt(5),sqrt(5)/(4)`.
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