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

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

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

We move all terms to the left:

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


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



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

t∈R


We get rid of parentheses

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

We calculate fractions


3t/6t^2+(-4t)/6t^2-1+3=0

We add all the numbers together, and all the variables

3t/6t^2+(-4t)/6t^2+2=0

We multiply all the terms by the denominator


3t+(-4t)+2*6t^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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