2/t=t/3t-4

Solution for 2/t=t/3t-4 equation:

2/t=t/3t-4

We move all terms to the left:

2/t-(t/3t-4)=0


Domain of the equation: t!=0

t∈R



Domain of the equation: 3t-4)!=0

t∈R


We get rid of parentheses

2/t-t/3t+4=0

We calculate fractions


(-1t^2)/3t^2+6t/3t^2+4=0

We multiply all the terms by the denominator


(-1t^2)+6t+4*3t^2=0

Wy multiply elements

(-1t^2)+12t^2+6t=0

We get rid of parentheses

-1t^2+12t^2+6t=0

We add all the numbers together, and all the variables

11t^2+6t=0

a = 11; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·11·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*11}=\frac{-12}{22}
=-6/11
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*11}=\frac{0}{22}
=0
$