1/4t+1/7t=1

Solution for 1/4t+1/7t=1 equation:

1/4t+1/7t=1

We move all terms to the left:

1/4t+1/7t-(1)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R



Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R


We calculate fractions


7t/28t^2+4t/28t^2-1=0

We multiply all the terms by the denominator


7t+4t-1*28t^2=0

We add all the numbers together, and all the variables

11t-1*28t^2=0

Wy multiply elements

-28t^2+11t=0

a = -28; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-28)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-28}=\frac{-22}{-56}
=11/28
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-28}=\frac{0}{-56}
=0
$