3/5t-1/10t=-19/2

Solution for 3/5t-1/10t=-19/2 equation:

3/5t-1/10t=-19/2

We move all terms to the left:

3/5t-1/10t-(-19/2)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R



Domain of the equation: 10t!=0

t!=0/10

t!=0

t∈R


We get rid of parentheses

3/5t-1/10t+19/2=0

We calculate fractions


950t^2/200t^2+120t/200t^2+(-20t)/200t^2=0

We multiply all the terms by the denominator


950t^2+120t+(-20t)=0

We get rid of parentheses

950t^2+120t-20t=0

We add all the numbers together, and all the variables

950t^2+100t=0

a = 950; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·950·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*950}=\frac{-200}{1900}
=-2/19
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*950}=\frac{0}{1900}
=0
$