4/7t-1/14t=-5/2

Solution for 4/7t-1/14t=-5/2 equation:

4/7t-1/14t=-5/2

We move all terms to the left:

4/7t-1/14t-(-5/2)=0


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R



Domain of the equation: 14t!=0

t!=0/14

t!=0

t∈R


We get rid of parentheses

4/7t-1/14t+5/2=0

We calculate fractions


490t^2/392t^2+224t/392t^2+(-28t)/392t^2=0

We multiply all the terms by the denominator


490t^2+224t+(-28t)=0

We get rid of parentheses

490t^2+224t-28t=0

We add all the numbers together, and all the variables

490t^2+196t=0

a = 490; b = 196; c = 0;
Δ = b2-4ac
Δ = 1962-4·490·0
Δ = 38416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38416}=196$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-196}{2*490}=\frac{-392}{980}
=-2/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+196}{2*490}=\frac{0}{980}
=0
$