T(n)=-15+1/2n

Solution for T(n)=-15+1/2n equation:

(T)=-15+1/2T

We move all terms to the left:

(T)-(-15+1/2T)=0


Domain of the equation: 2T)!=0

T!=0/1

T!=0

T∈R


We add all the numbers together, and all the variables

T-(1/2T-15)=0

We get rid of parentheses

T-1/2T+15=0

We multiply all the terms by the denominator


T*2T+15*2T-1=0

Wy multiply elements

2T^2+30T-1=0

a = 2; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·2·(-1)
Δ = 908
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{227}}{2*2}=\frac{-30-2\sqrt{227}}{4}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{227}}{2*2}=\frac{-30+2\sqrt{227}}{4}
$