1/2t=2/3t+4

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

1/2t=2/3t+4

We move all terms to the left:

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


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 3t+4)!=0

t∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-24t^2+3t+(-4t)=0

We get rid of parentheses

-24t^2+3t-4t=0

We add all the numbers together, and all the variables

-24t^2-1t=0

a = -24; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-24)·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*-24}=\frac{0}{-48}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-24}=\frac{2}{-48}
=-1/24
$