2+1/3t=1+1/5t

Solution for 2+1/3t=1+1/5t equation:

2+1/3t=1+1/5t

We move all terms to the left:

2+1/3t-(1+1/5t)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 5t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

1/3t-(1/5t+1)+2=0

We get rid of parentheses

1/3t-1/5t-1+2=0

We calculate fractions


5t/15t^2+(-3t)/15t^2-1+2=0

We add all the numbers together, and all the variables

5t/15t^2+(-3t)/15t^2+1=0

We multiply all the terms by the denominator


5t+(-3t)+1*15t^2=0

Wy multiply elements

15t^2+5t+(-3t)=0

We get rid of parentheses

15t^2+5t-3t=0

We add all the numbers together, and all the variables

15t^2+2t=0

a = 15; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·15·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*15}=\frac{-4}{30}
=-2/15
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*15}=\frac{0}{30}
=0
$