2/t = t/5t-12?

Question

please show step by step solution

Answer 1

Cross-multiplication
2*(5t-12) = t*t
10t - 24 = t^2
t^2 - 10t + 24 = 0
(t-6)(t-4) = 0

t = 6 , t = 4

Answer 2

I do not know if 12 isin the denominator so I give you two possibilities
1) 12 is a number not in the denominator
multiply all expression by 5t

10 = t -60t

10 = -59 t t= -10/59

2) you mean 2/t = t/(5t-12)

in that case remember a/b = c/d implies ab=cd

t^2 = 10t -24

t^2 -10t +24 =0

the roots are t=6 and t=-4

Answer 3

First, multiply through the whole equation by 5t, the common denominator, in order to clear the equation of fractions:
10 = t - 12
Now, add 12 to both sides:
22 = t

Answer 4

I assume you mean 2/t = t/(5t-12) ?
2=(t/(5t-12)) t
2=t^2/(5t-12)
2(5t-12)=t^2
10t-24=t^2
t^2-10t+24=0
t=4 or t=6
am I missing something?

Answer 5

2/t = t/5t-12 cancel t in numerator & denominator
2/t=1/5-12 combine like terms
2/t=11.8 multiply both sides by t
2=11.8t divide both sides by 11.8
t=2/11.8 perform the division
t=.1695

Answer 6

2/t=t/(5t-12)
we can write it :
2*(5t-12)=t*t
> 10*t-24 =t*t
>> 0 =t^2-10t+24
then we must to solve this equation:
a^2+b+c=0
a=1,b=-10,c=+24
delta=(-10)^2-4*1*(+24)
.delta=100-96=4

t1=(-b-radica(delta))/2=(10+2)/2=6
t2=(-b+radica(delta))/2=(10-2)/2=4