2t/t-5+5/3t=-4/3

Solution for 2t/t-5+5/3t=-4/3 equation:

2t/t-5+5/3t=-4/3

We move all terms to the left:

2t/t-5+5/3t-(-4/3)=0


Domain of the equation: t!=0

t∈R



Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We get rid of parentheses

2t/t+5/3t-5+4/3=0

We calculate fractions


54t^2/27t^2+5t/27t^2+4t/27t^2-5=0

We multiply all the terms by the denominator


54t^2+5t+4t-5*27t^2=0

We add all the numbers together, and all the variables

54t^2+9t-5*27t^2=0

Wy multiply elements

54t^2-135t^2+9t=0

We add all the numbers together, and all the variables

-81t^2+9t=0

a = -81; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-81)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-81}=\frac{-18}{-162}
=1/9
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-81}=\frac{0}{-162}
=0
$