2/3t+5/6t=27

Solution for 2/3t+5/6t=27 equation:

2/3t+5/6t=27

We move all terms to the left:

2/3t+5/6t-(27)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 6t!=0

t!=0/6

t!=0

t∈R


We calculate fractions


12t/18t^2+15t/18t^2-27=0

We multiply all the terms by the denominator


12t+15t-27*18t^2=0

We add all the numbers together, and all the variables

27t-27*18t^2=0

Wy multiply elements

-486t^2+27t=0

a = -486; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-486)·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*-486}=\frac{-54}{-972}
=1/18
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-486}=\frac{0}{-972}
=0
$