1/6t+1/8t=1

Solution for 1/6t+1/8t=1 equation:

1/6t+1/8t=1

We move all terms to the left:

1/6t+1/8t-(1)=0


Domain of the equation: 6t!=0

t!=0/6

t!=0

t∈R



Domain of the equation: 8t!=0

t!=0/8

t!=0

t∈R


We calculate fractions


8t/48t^2+6t/48t^2-1=0

We multiply all the terms by the denominator


8t+6t-1*48t^2=0

We add all the numbers together, and all the variables

14t-1*48t^2=0

Wy multiply elements

-48t^2+14t=0

a = -48; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-48)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-48}=\frac{-28}{-96}
=7/24
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-48}=\frac{0}{-96}
=0
$