5/7t-1/3t-27=17

Solution for 5/7t-1/3t-27=17 equation:

5/7t-1/3t-27=17

We move all terms to the left:

5/7t-1/3t-27-(17)=0


Domain of the equation: 7t!=0

t!=0/7

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

5/7t-1/3t-44=0

We calculate fractions


15t/21t^2+(-7t)/21t^2-44=0

We multiply all the terms by the denominator


15t+(-7t)-44*21t^2=0

Wy multiply elements

-924t^2+15t+(-7t)=0

We get rid of parentheses

-924t^2+15t-7t=0

We add all the numbers together, and all the variables

-924t^2+8t=0

a = -924; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-924)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-924}=\frac{-16}{-1848}
=2/231
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-924}=\frac{0}{-1848}
=0
$