T(n)=T(6n/10)+n

Solution for T(n)=T(6n/10)+n equation:

(T)=(6T/10)+T

We move all terms to the left:

(T)-((6T/10)+T)=0


Domain of the equation: 10)+T)!=0

T!=0/1

T!=0

T∈R


We add all the numbers together, and all the variables

T-((+6T/10)+T)=0

We multiply all the terms by the denominator


T*10)+T)-((+6T=0

We add all the numbers together, and all the variables

6T+T*10)+T)-((=0

Wy multiply elements

10T^2+6T=0

a = 10; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·10·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*10}=\frac{-12}{20}
=-3/5
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*10}=\frac{0}{20}
=0
$