Question

Solve the quadratic equation 9x^2+6x=4 by using quadratic formula

Answer 1

x = (-1 - √5)/2

Or

x = (-1 + √5)/2

Step-By-Step-Explanation

Given :-

9x² + 6x = 4

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To Find :-

We have to solve the quadratic equation by using quadratic formula.

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Solution :-

Given that,

9x² + 6x = 4 ........ (1)

From equation 1, we get

9x² + 6x - 4 = 0

Now, We know quadratic formula

Quadratic Formula = (-b ± √D)/2a

Where,

√D = √(b² - 4ac)

a = 9

b = 6

c = -4

(Putting Values)

$x = \frac{ - 6 \pm \sqrt{( {6)}^{2} - 4(9)( - 4)} }{2(9)} \\ \\ x = \frac{ - 6 \pm \sqrt{36 - 36( - 4)} }{12} \\ \\ x = \frac{ - 6 \pm \sqrt{36 - ( - 144)} }{12} \\ \\ x = \frac{ -6 \pm \sqrt{36 + 144} }{12} \\ \\ x = \frac{ - 6 \pm \sqrt{180} }{12} \\ \\ x = \frac{ - 6 \pm6 \sqrt{5} }{12} \\ \\ x = \frac{- 6 - 6 \sqrt{5}}{12} \\ \\ x = \frac{6( - 1 - \sqrt{5} )}{12} \\ \\ x = \frac{ - 1 - \sqrt{5} }{2} \\ \\ \bf{or} \\ \\ x = \frac{ - 6 + 6 \sqrt{5} }{12} \\ \\ x = \frac{ 6( - 1 + \sqrt{5})}{12} \\ \\ x = \frac{ - 1 + \sqrt{5} }{2}$