2/3t+1/5t=2

Solution for 2/3t+1/5t=2 equation:

2/3t+1/5t=2

We move all terms to the left:

2/3t+1/5t-(2)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R


We calculate fractions


10t/15t^2+3t/15t^2-2=0

We multiply all the terms by the denominator


10t+3t-2*15t^2=0

We add all the numbers together, and all the variables

13t-2*15t^2=0

Wy multiply elements

-30t^2+13t=0

a = -30; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-30)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-30}=\frac{-26}{-60}
=13/30
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-30}=\frac{0}{-60}
=0
$