21+2/3t=50-11/12t

Solution for 21+2/3t=50-11/12t equation:

21+2/3t=50-11/12t

We move all terms to the left:

21+2/3t-(50-11/12t)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 12t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

2/3t-(-11/12t+50)+21=0

We get rid of parentheses

2/3t+11/12t-50+21=0

We calculate fractions


24t/36t^2+33t/36t^2-50+21=0

We add all the numbers together, and all the variables

24t/36t^2+33t/36t^2-29=0

We multiply all the terms by the denominator


24t+33t-29*36t^2=0

We add all the numbers together, and all the variables

57t-29*36t^2=0

Wy multiply elements

-1044t^2+57t=0

a = -1044; b = 57; c = 0;
Δ = b2-4ac
Δ = 572-4·(-1044)·0
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-57}{2*-1044}=\frac{-114}{-2088}
=19/348
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+57}{2*-1044}=\frac{0}{-2088}
=0
$