G(x)=3x-8/x-3

Solution for G(x)=3x-8/x-3 equation:

(G)=3G-8/G-3

We move all terms to the left:

(G)-(3G-8/G-3)=0


Domain of the equation: G-3)!=0

G∈R


We get rid of parentheses

G-3G+8/G+3=0

We multiply all the terms by the denominator


G*G-3G*G+3*G+8=0

We add all the numbers together, and all the variables

3G+G*G-3G*G+8=0

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = 3; c = +8;
Δ = b2-4ac
Δ = 32-4·(-2)·8
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{73}}{2*-2}=\frac{-3-\sqrt{73}}{-4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{73}}{2*-2}=\frac{-3+\sqrt{73}}{-4}
$