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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)!=0We add all the numbers together, and all the variables
t!=0/1
t!=0
t∈R
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 $
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