1/8t+1/12t=1

Solution for 1/8t+1/12t=1 equation:

1/8t+1/12t=1

We move all terms to the left:

1/8t+1/12t-(1)=0


Domain of the equation: 8t!=0

t!=0/8

t!=0

t∈R



Domain of the equation: 12t!=0

t!=0/12

t!=0

t∈R


We calculate fractions


12t/96t^2+8t/96t^2-1=0

We multiply all the terms by the denominator


12t+8t-1*96t^2=0

We add all the numbers together, and all the variables

20t-1*96t^2=0

Wy multiply elements

-96t^2+20t=0

a = -96; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-96)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-96}=\frac{-40}{-192}
=5/24
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-96}=\frac{0}{-192}
=0
$