G(x)=7-1/2x+9

Solution for G(x)=7-1/2x+9 equation:

(G)=7-1/2G+9

We move all terms to the left:

(G)-(7-1/2G+9)=0


Domain of the equation: 2G+9)!=0

G∈R


We add all the numbers together, and all the variables

G-(-1/2G+16)=0

We get rid of parentheses

G+1/2G-16=0

We multiply all the terms by the denominator


G*2G-16*2G+1=0

Wy multiply elements

2G^2-32G+1=0

a = 2; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·2·1
Δ = 1016
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:

$\sqrt{\Delta}=\sqrt{1016}=\sqrt{4*254}=\sqrt{4}*\sqrt{254}=2\sqrt{254}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{254}}{2*2}=\frac{32-2\sqrt{254}}{4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{254}}{2*2}=\frac{32+2\sqrt{254}}{4}
$