5/t+1/3t-27=17

Solution for 5/t+1/3t-27=17 equation:

5/t+1/3t-27=17

We move all terms to the left:

5/t+1/3t-27-(17)=0


Domain of the equation: t!=0

t∈R



Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

5/t+1/3t-44=0

We calculate fractions


15t/3t^2+t/3t^2-44=0

We multiply all the terms by the denominator


15t+t-44*3t^2=0

We add all the numbers together, and all the variables

16t-44*3t^2=0

Wy multiply elements

-132t^2+16t=0

a = -132; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-132)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-132}=\frac{-32}{-264}
=4/33
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-132}=\frac{0}{-264}
=0
$