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

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

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

We move all terms to the left:

5/7t-1/3t-27-(27)=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-54=0

We calculate fractions


15t/21t^2+(-7t)/21t^2-54=0

We multiply all the terms by the denominator


15t+(-7t)-54*21t^2=0

Wy multiply elements

-1134t^2+15t+(-7t)=0

We get rid of parentheses

-1134t^2+15t-7t=0

We add all the numbers together, and all the variables

-1134t^2+8t=0

a = -1134; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-1134)·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*-1134}=\frac{-16}{-2268}
=4/567
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-1134}=\frac{0}{-2268}
=0
$