# What is x if 4x+3/x-9=5?

Oct 29, 2015

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

Subtracting 5x from both sides

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

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

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

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

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a} =$

$x = \frac{- \left(- 14\right) \pm \sqrt{\left(- {14}^{2}\right) - \left(4 \cdot 4 \cdot 3\right)}}{2 \cdot 4}$

$x = \frac{14 \pm \sqrt{196 - 48}}{8} =$

$x = \frac{14 \pm \sqrt{148}}{8}$

Solve for $x$.

$x = \frac{14 + \sqrt{148}}{8} , \frac{14 - \sqrt{145}}{8}$