Question

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

Answer 1

`(15 +- 3sqrt29)/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 - 4ac = 900 + 144 = 1044 = 36(29)`--> `d = +- 6sqrt29`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = -30/-8 +- (6sqrt29)/8 = (15 +- 3sqrt29)/4`

Answer 2

`x = 7.7889 or 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.

`color(red)(x xx) -4x +(color(red)(x xx)9)/x=color(red)(x xx)-30`

`-4x^2 + 9 =-30x" re-arrange and make" =0`

`0 = 4x^2 -30x-9" does not factorise"`

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

`x = (-b+-sqrt(b^2-4ac))/(2a)`

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

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

`x = (30+-sqrt(1044))/(8)`

`x = 7.7889 or x = -0.2889`