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

Wy multiply elements

-30t^2+10t+(-3t)=0

We get rid of parentheses

-30t^2+10t-3t=0

We add all the numbers together, and all the variables

-30t^2+7t=0

a = -30; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-30)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-30}=\frac{-14}{-60}
=7/30
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-30}=\frac{0}{-60}
=0
$