2/9t-5/7=1/12t

Solution for 2/9t-5/7=1/12t equation:

2/9t-5/7=1/12t

We move all terms to the left:

2/9t-5/7-(1/12t)=0


Domain of the equation: 9t!=0

t!=0/9

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

2/9t-(+1/12t)-5/7=0

We get rid of parentheses

2/9t-1/12t-5/7=0

We calculate fractions


(-540t^2)/5292t^2+1176t/5292t^2+(-441t)/5292t^2=0

We multiply all the terms by the denominator


(-540t^2)+1176t+(-441t)=0

We get rid of parentheses

-540t^2+1176t-441t=0

We add all the numbers together, and all the variables

-540t^2+735t=0

a = -540; b = 735; c = 0;
Δ = b2-4ac
Δ = 7352-4·(-540)·0
Δ = 540225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{540225}=735$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(735)-735}{2*-540}=\frac{-1470}{-1080}
=1+13/36
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(735)+735}{2*-540}=\frac{0}{-1080}
=0
$