G(t)=4t-8/t-2

Solution for G(t)=4t-8/t-2 equation:

(G)=4G-8/G-2

We move all terms to the left:

(G)-(4G-8/G-2)=0


Domain of the equation: G-2)!=0

G∈R


We get rid of parentheses

G-4G+8/G+2=0

We multiply all the terms by the denominator


G*G-4G*G+2*G+8=0

We add all the numbers together, and all the variables

2G+G*G-4G*G+8=0

Wy multiply elements

G^2-4G^2+2G+8=0

We add all the numbers together, and all the variables

-3G^2+2G+8=0

a = -3; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-3)·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*-3}=\frac{-12}{-6}
=+2
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*-3}=\frac{8}{-6}
=-1+1/3
$