G(x)=2x-15/6x+8

Solution for G(x)=2x-15/6x+8 equation:

(G)=2G-15/6G+8

We move all terms to the left:

(G)-(2G-15/6G+8)=0


Domain of the equation: 6G+8)!=0

G∈R


We get rid of parentheses

G-2G+15/6G-8=0

We multiply all the terms by the denominator


G*6G-2G*6G-8*6G+15=0

Wy multiply elements

6G^2-12G^2-48G+15=0

We add all the numbers together, and all the variables

-6G^2-48G+15=0

a = -6; b = -48; c = +15;
Δ = b2-4ac
Δ = -482-4·(-6)·15
Δ = 2664
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:

$\sqrt{\Delta}=\sqrt{2664}=\sqrt{36*74}=\sqrt{36}*\sqrt{74}=6\sqrt{74}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-6\sqrt{74}}{2*-6}=\frac{48-6\sqrt{74}}{-12}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+6\sqrt{74}}{2*-6}=\frac{48+6\sqrt{74}}{-12}
$