1/7t+1/3t=1

Solution for 1/7t+1/3t=1 equation:

1/7t+1/3t=1

We move all terms to the left:

1/7t+1/3t-(1)=0


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R



Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We calculate fractions


3t/21t^2+7t/21t^2-1=0

We multiply all the terms by the denominator


3t+7t-1*21t^2=0

We add all the numbers together, and all the variables

10t-1*21t^2=0

Wy multiply elements

-21t^2+10t=0

a = -21; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-21)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-21}=\frac{-20}{-42}
=10/21
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-21}=\frac{0}{-42}
=0
$