5/6t+2/3t=3

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

5/6t+2/3t=3

We move all terms to the left:

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


Domain of the equation: 6t!=0

t!=0/6

t!=0

t∈R



Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We calculate fractions


15t/18t^2+12t/18t^2-3=0

We multiply all the terms by the denominator


15t+12t-3*18t^2=0

We add all the numbers together, and all the variables

27t-3*18t^2=0

Wy multiply elements

-54t^2+27t=0

a = -54; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-54)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-54}=\frac{-54}{-108}
=1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-54}=\frac{0}{-108}
=0
$