G(8)=x-10/2x+6

Solution for G(8)=x-10/2x+6 equation:

(8)=G-10/2G+6

We move all terms to the left:

(8)-(G-10/2G+6)=0


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

G∈R


We get rid of parentheses

-G+10/2G-6+8=0

We multiply all the terms by the denominator


-G*2G-6*2G+8*2G+10=0

Wy multiply elements

-2G^2-12G+16G+10=0

We add all the numbers together, and all the variables

-2G^2+4G+10=0

a = -2; b = 4; c = +10;
Δ = b2-4ac
Δ = 42-4·(-2)·10
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*-2}=\frac{-4-4\sqrt{6}}{-4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*-2}=\frac{-4+4\sqrt{6}}{-4}
$