# What is x if -4x+9/x=-30?

Jul 31, 2016

$\frac{15 \pm 3 \sqrt{29}}{4}$

#### Explanation:

Multiply both sides of the equation by x -->
-4x^2 + 9 = - 30x
y = - 4x^2 + 30x + 9 = 0
Solve this equation by the new quadratic formula in graphic form (Socratic Search).
$D = {b}^{2} = {b}^{2} - 4 a c = 900 + 144 = 1044 = 36 \left(29\right)$--> $d = \pm 6 \sqrt{29}$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{30}{-} 8 \pm \frac{6 \sqrt{29}}{8} = \frac{15 \pm 3 \sqrt{29}}{4}$

Jul 31, 2016

$x = 7.7889 \mathmr{and} x = - 0.2889$

#### Explanation:

The fact that $x$ is in the denominator already means that we assume it is not equal to 0.

Multiply all the terms by $x$ to get rid of the fraction.

$\textcolor{red}{x \times} - 4 x + \frac{\textcolor{red}{x \times} 9}{x} = \textcolor{red}{x \times} - 30$

$- 4 {x}^{2} + 9 = - 30 x \text{ re-arrange and make} = 0$

$0 = 4 {x}^{2} - 30 x - 9 \text{ does not factorise}$

Use the formula: $a = 4 , b = - 30 , c = - 9$

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

x = ((-(-30)+-sqrt((-30)^2-4(4)(-9))))/(2(4)

x = (30+-sqrt(900+144))/(8))

$x = \frac{30 \pm \sqrt{1044}}{8}$

$x = 7.7889 \mathmr{and} x = - 0.2889$