3t-2/4-(2t+3)/3=(5/6)-t

Solution for 3t-2/4-(2t+3)/3=(5/6)-t equation:

3t-2/4-(2t+3)/3=(5/6)-t

We move all terms to the left:

3t-2/4-(2t+3)/3-((5/6)-t)=0


Domain of the equation: 6)-t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

3t-(2t+3)/3-((+5/6)-t)-2/4=0

We calculate fractions


(-72t^2-8t)/72t+3t+()/72t+(-216t)/72t=0

We multiply all the terms by the denominator


(-72t^2-8t)+3t*72t+(-216t)+()=0

We add all the numbers together, and all the variables

(-72t^2-8t)+3t*72t+(-216t)=0

Wy multiply elements

(-72t^2-8t)+216t^2+(-216t)=0

We get rid of parentheses

-72t^2+216t^2-8t-216t=0

We add all the numbers together, and all the variables

144t^2-224t=0

a = 144; b = -224; c = 0;
Δ = b2-4ac
Δ = -2242-4·144·0
Δ = 50176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50176}=224$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-224}{2*144}=\frac{0}{288}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+224}{2*144}=\frac{448}{288}
=1+5/9
$