How to solve this quadratic equation?

Question

100/(x+30) = 100/x - 1/6

It's a question in my Math textbook.I'm practising the questions inside for revision, and my brain just isn't working...I've been doing Math questions for a few hours already...
Could someone show me the steps so I can understand the way to solve it?

Thanks for any help. :)

Answer 1

(x+30)(x)(6)(100/(x+30)) = (x+30)(x)(6)(100/x -1/6)
600x =600x +18000 - x2 - 30x
0 = 18000 -30x - x2
x2 +30x - 18000 = 0
(x+150)(x-120) =0
x = -150 x = 120

Answer 2

First, get rid of all your fractions.

Multiply by (x+30)

100=100(x+30)/x-(x+30)/6
100=(100x+3000)/x-(x+30)/6

Multiply by x

100x=100x+3000-(x^2+30x)/6

Multiply by 6

600x=600x+18000-x^2-30x

Take 600x from both sides

0=-x^2-30x+18000

Swap the two sides over

-x^2-30x+18000=0

Use the quadratic formula

x=(-b±√(b^2-4ac))/2a)
=(30±√(-30^2-4*(-1)*(18000)))/2*(-1)
=(30±√(900--72000))/-2
=(30±√72900)/-2
=(30-270)/-2 or (30+270)/-2
=-240/-2 or 300/-2
=-150 or 120

Sorry for my mistake earlier!

Answer 3

It goes like this :-

100 / (x+30) = (600 - x) / 6x

On cross multiplying:
(x+30)(600-x) = 600x

On multiplting and then solving, we get :-
-x ^2 - 30x +18000 = 0
solve as usual

Answer 4

100/(x+30) = 100/x - 1/6
Left and right *6x(x+30)
600x = 600(x+30) - x(x+30)
Now it is free from fractions
600x = 600x +18,000 - x2 -3x
0 = 18,000 - x2 -3x
x2 +3x - 18000 = 0
D = 9 + 4*18000 = 72009
x = (-3 - root72009)/2 or x = (-3 + root72009)/2

Answer 5

Multiply both sides by 'x' and 'x+30'. Solve for x as normal.

Note. X cannot be 0 or -30 because that would make one of the fractions undefined (infinity).

Answer 6

Well, I can give it a shot.
100(x+30)=100/x-1/6
100x+3000=600-x/6x
6x(100x+3000)=600-x
600x2(square)+1800x=600-x
600x2(square)+1800x+x-600=0
600x2(square)+1900x-600=0

now u can solve it by splitting the mid term
n hey if u stil need help, lemme now

Answer 7

100/(x+30)=100*6-x/6x
100/(x+30)=600-x/6x
100*6x=(600-x)(x+30)
600x=600x+18000-x*x-30x
600x-600x=18000-x*x-30x
x*x+30x-18000=0
x*x+150x-120x-18000=0
x(x+150)-120(x+150)=0
(x-120)(x+150)=0
x=120 or x=-150