G(x)=6x+12/6x+24

Solution for G(x)=6x+12/6x+24 equation:

(G)=6G+12/6G+24

We move all terms to the left:

(G)-(6G+12/6G+24)=0


Domain of the equation: 6G+24)!=0

G∈R


We get rid of parentheses

G-6G-12/6G-24=0

We multiply all the terms by the denominator


G*6G-6G*6G-24*6G-12=0

Wy multiply elements

6G^2-36G^2-144G-12=0

We add all the numbers together, and all the variables

-30G^2-144G-12=0

a = -30; b = -144; c = -12;
Δ = b2-4ac
Δ = -1442-4·(-30)·(-12)
Δ = 19296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{19296}=\sqrt{144*134}=\sqrt{144}*\sqrt{134}=12\sqrt{134}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-12\sqrt{134}}{2*-30}=\frac{144-12\sqrt{134}}{-60}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+12\sqrt{134}}{2*-30}=\frac{144+12\sqrt{134}}{-60}
$