1/3t=-t+2/3t-1

Solution for 1/3t=-t+2/3t-1 equation:

1/3t=-t+2/3t-1

We move all terms to the left:

1/3t-(-t+2/3t-1)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 3t-1)!=0

t∈R


We add all the numbers together, and all the variables

1/3t-(-1t+2/3t-1)=0

We get rid of parentheses

1/3t+1t-2/3t+1=0

We multiply all the terms by the denominator


1t*3t+1*3t+1-2=0

We add all the numbers together, and all the variables

1t*3t+1*3t-1=0

Wy multiply elements

3t^2+3t-1=0

a = 3; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·3·(-1)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{21}}{2*3}=\frac{-3-\sqrt{21}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{21}}{2*3}=\frac{-3+\sqrt{21}}{6}
$