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

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

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

We move all terms to the left:

2+2/3t-(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

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

We get rid of parentheses

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

We calculate fractions


8t/12t^2+(-3t)/12t^2-1+2=0

We add all the numbers together, and all the variables

8t/12t^2+(-3t)/12t^2+1=0

We multiply all the terms by the denominator


8t+(-3t)+1*12t^2=0

Wy multiply elements

12t^2+8t+(-3t)=0

We get rid of parentheses

12t^2+8t-3t=0

We add all the numbers together, and all the variables

12t^2+5t=0

a = 12; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·12·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*12}=\frac{-10}{24}
=-5/12
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*12}=\frac{0}{24}
=0
$