2/t=t/5t-12
what is it 2 is t and is it (5*2)-12 or (5/2)-12
2/t eqauls t over 5t-12
I will read it as
2/t = t/(5t-12)
if so , then
t^2 = 10t - 24
t^2 - 10t + 24 = 0
(t-4)(t-6) = 0
t = 4 or t = 6
To solve the equation 2/t = t/(5t - 12), we can follow these steps:
Step 1: Clear the denominators by multiplying both sides of the equation by t(5t - 12). This will eliminate the fractions.
t(5t - 12) * (2/t) = t(5t - 12) * (t/(5t - 12))
Now we have:
2(5t - 12) = t^2
Step 2: Distribute 2 to the terms inside the parentheses on the left side:
10t - 24 = t^2
Step 3: Rearrange the equation to form a quadratic equation with 0 on one side:
t^2 - 10t + 24 = 0
Step 4: Factor or use the quadratic formula to solve the quadratic equation:
In this case, the equation can be factored as:
(t - 6)(t - 4) = 0
Setting each factor equal to zero, we have:
t - 6 = 0 or t - 4 = 0
Solving each equation gives us:
t = 6 or t = 4
Therefore, the solutions to the given equation are t = 6 and t = 4.