3/2t-1/5t=2

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

3/2t-1/5t=2

We move all terms to the left:

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


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R


We calculate fractions


15t/10t^2+(-2t)/10t^2-2=0

We multiply all the terms by the denominator


15t+(-2t)-2*10t^2=0

Wy multiply elements

-20t^2+15t+(-2t)=0

We get rid of parentheses

-20t^2+15t-2t=0

We add all the numbers together, and all the variables

-20t^2+13t=0

a = -20; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-20)·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*-20}=\frac{-26}{-40}
=13/20
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-20}=\frac{0}{-40}
=0
$