G(t)=t/2t+6

Solution for G(t)=t/2t+6 equation:

(G)=G/2G+6

We move all terms to the left:

(G)-(G/2G+6)=0


Domain of the equation: 2G+6)!=0

G∈R


We get rid of parentheses

G-G/2G-6=0

We multiply all the terms by the denominator


G*2G-G-6*2G=0

We add all the numbers together, and all the variables

-1G+G*2G-6*2G=0

Wy multiply elements

2G^2-1G-12G=0

We add all the numbers together, and all the variables

2G^2-13G=0

a = 2; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·2·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*2}=\frac{0}{4}
=0
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*2}=\frac{26}{4}
=6+1/2
$