5/6t-3/4t+3/4=-1/2

Solution for 5/6t-3/4t+3/4=-1/2 equation:

5/6t-3/4t+3/4=-1/2

We move all terms to the left:

5/6t-3/4t+3/4-(-1/2)=0


Domain of the equation: 6t!=0

t!=0/6

t!=0

t∈R



Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We get rid of parentheses

5/6t-3/4t+3/4+1/2=0

We calculate fractions


384t^2/768t^2+640t/768t^2+(-72t)/768t^2+72t/768t^2=0

We multiply all the terms by the denominator


384t^2+640t+(-72t)+72t=0

We add all the numbers together, and all the variables

384t^2+712t+(-72t)=0

We get rid of parentheses

384t^2+712t-72t=0

We add all the numbers together, and all the variables

384t^2+640t=0

a = 384; b = 640; c = 0;
Δ = b2-4ac
Δ = 6402-4·384·0
Δ = 409600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{409600}=640$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(640)-640}{2*384}=\frac{-1280}{768}
=-1+2/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(640)+640}{2*384}=\frac{0}{768}
=0
$