1/30t+1/20t=1

Solution for 1/30t+1/20t=1 equation:

1/30t+1/20t=1

We move all terms to the left:

1/30t+1/20t-(1)=0


Domain of the equation: 30t!=0

t!=0/30

t!=0

t∈R



Domain of the equation: 20t!=0

t!=0/20

t!=0

t∈R


We calculate fractions


20t/600t^2+30t/600t^2-1=0

We multiply all the terms by the denominator


20t+30t-1*600t^2=0

We add all the numbers together, and all the variables

50t-1*600t^2=0

Wy multiply elements

-600t^2+50t=0

a = -600; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-600)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*-600}=\frac{-100}{-1200}
=1/12
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-600}=\frac{0}{-1200}
=0
$