5/7t+1/3t-27=13

Solution for 5/7t+1/3t-27=13 equation:

5/7t+1/3t-27=13

We move all terms to the left:

5/7t+1/3t-27-(13)=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-40=0

We calculate fractions


15t/21t^2+7t/21t^2-40=0

We multiply all the terms by the denominator


15t+7t-40*21t^2=0

We add all the numbers together, and all the variables

22t-40*21t^2=0

Wy multiply elements

-840t^2+22t=0

a = -840; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-840)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-840}=\frac{-44}{-1680}
=11/420
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-840}=\frac{0}{-1680}
=0
$