1/4t+1/3t=1

Solution for 1/4t+1/3t=1 equation:

1/4t+1/3t=1

We move all terms to the left:

1/4t+1/3t-(1)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R



Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We calculate fractions


3t/12t^2+4t/12t^2-1=0

We multiply all the terms by the denominator


3t+4t-1*12t^2=0

We add all the numbers together, and all the variables

7t-1*12t^2=0

Wy multiply elements

-12t^2+7t=0

a = -12; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-12)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-12}=\frac{-14}{-24}
=7/12
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-12}=\frac{0}{-24}
=0
$