1/4t+1/6t=1

Solution for 1/4t+1/6t=1 equation:

1/4t+1/6t=1

We move all terms to the left:

1/4t+1/6t-(1)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R



Domain of the equation: 6t!=0

t!=0/6

t!=0

t∈R


We calculate fractions


6t/24t^2+4t/24t^2-1=0

We multiply all the terms by the denominator


6t+4t-1*24t^2=0

We add all the numbers together, and all the variables

10t-1*24t^2=0

Wy multiply elements

-24t^2+10t=0

a = -24; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-24)·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*-24}=\frac{-20}{-48}
=5/12
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-24}=\frac{0}{-48}
=0
$