T(n)=T(2n/3)+1

Solution for T(n)=T(2n/3)+1 equation:

(T)=(2T/3)+1

We move all terms to the left:

(T)-((2T/3)+1)=0

We add all the numbers together, and all the variables

T-((+2T/3)+1)=0

We multiply all the terms by the denominator


T*3)+1)-((+2T=0

We add all the numbers together, and all the variables

2T+T*3)+1)-((=0

Wy multiply elements

3T^2+2T=0

a = 3; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·3·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*3}=\frac{-4}{6}
=-2/3
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*3}=\frac{0}{6}
=0
$