What is x if $4 x + \frac{3}{x} - 9 = 5$ $4x+3/x-9=5$ ?

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What is x if $4 x + \frac{3}{x} - 9 = 5$ $4x+3/x-9=5$ ?

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Answer 1 · 2015-10-29T04:16:59

4x + 3/x -9 = 5

multiplying both the sides with x

x ( 4x + 3/x -9) = 5.x

4x.x + 3/x .x -9.x = 5.x

4 $x^{2}$ $x^2$ +3 - 9x = 5x

Subtracting 5x from both sides

4 $x^{2}$ $x^2$ +3 - 9x -5x = 5x -5x

4 $x^{2}$ $x^2$ +3 -14x = 0

4 $x^{2}$ $x^2$ -14x + 3 = 0

Apply the quadratic formula.

$4 x^{2} - 14 x + 3$ $4x^2-14x+3$ is in the form of a quadratic equation $a^{2} x + b x + c$ $a^2x+bx+c$ , where $a = 4, b = - 14, and c = 3$ $a=4, b=-14, and c=3$ .

Quadratic Formula

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} =$ $x=(-b+-sqrt(b^2-4ac))/(2a)=$

$x = \frac{- (- 14) \pm \sqrt{(- 14^{2}) - (4 \cdot 4 \cdot 3)}}{2 \cdot 4}$ $x=(-(-14)+-sqrt((-14^2)-(4*4*3)))/(2*4)$

$x = \frac{14 \pm \sqrt{196 - 48}}{8} =$ $x=(14+-sqrt(196-48))/8=$

$x = \frac{14 \pm \sqrt{148}}{8}$ $x=(14+-sqrt(148))/8$

Solve for $x$ $x$ .

$x = \frac{14 + \sqrt{148}}{8}, \frac{14 - \sqrt{145}}{8}$ $x=(14+sqrt148)/8, (14-sqrt 145)/8$

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