4/3t=12-2t

Solution for 4/3t=12-2t equation:

4/3t=12-2t

We move all terms to the left:

4/3t-(12-2t)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/3t+2t-12=0

We multiply all the terms by the denominator


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

Wy multiply elements

6t^2-36t+4=0

a = 6; b = -36; c = +4;
Δ = b2-4ac
Δ = -362-4·6·4
Δ = 1200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-20\sqrt{3}}{2*6}=\frac{36-20\sqrt{3}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+20\sqrt{3}}{2*6}=\frac{36+20\sqrt{3}}{12}
$