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

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

(G)=-1/2G+9

We move all terms to the left:

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


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

G∈R


We get rid of parentheses

G+1/2G-9=0

We multiply all the terms by the denominator


G*2G-9*2G+1=0

Wy multiply elements

2G^2-18G+1=0

a = 2; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·2·1
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{79}}{2*2}=\frac{18-2\sqrt{79}}{4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{79}}{2*2}=\frac{18+2\sqrt{79}}{4}
$