T(n)=T(n/4)+1

Solution for T(n)=T(n/4)+1 equation:

(T)=(T/4)+1

We move all terms to the left:

(T)-((T/4)+1)=0

We add all the numbers together, and all the variables

T-((+T/4)+1)=0

We multiply all the terms by the denominator


T*4)+1)-((+T=0

We add all the numbers together, and all the variables

T+T*4)+1)-((=0

Wy multiply elements

4T^2+T=0

a = 4; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·4·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*4}=\frac{-2}{8}
=-1/4
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*4}=\frac{0}{8}
=0
$