1/3t+2=1+1/4t

Solution for 1/3t+2=1+1/4t equation:

1/3t+2=1+1/4t

We move all terms to the left:

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


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 4t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/3t-1/4t-1+2=0

We calculate fractions


4t/12t^2+(-3t)/12t^2-1+2=0

We add all the numbers together, and all the variables

4t/12t^2+(-3t)/12t^2+1=0

We multiply all the terms by the denominator


4t+(-3t)+1*12t^2=0

Wy multiply elements

12t^2+4t+(-3t)=0

We get rid of parentheses

12t^2+4t-3t=0

We add all the numbers together, and all the variables

12t^2+t=0

a = 12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·12·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*12}=\frac{-2}{24}
=-1/12
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*12}=\frac{0}{24}
=0
$