G(x)=1/2x+5

Solution for G(x)=1/2x+5 equation:

(G)=1/2G+5

We move all terms to the left:

(G)-(1/2G+5)=0


Domain of the equation: 2G+5)!=0

G∈R


We get rid of parentheses

G-1/2G-5=0

We multiply all the terms by the denominator


G*2G-5*2G-1=0

Wy multiply elements

2G^2-10G-1=0

a = 2; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·2·(-1)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{3}}{2*2}=\frac{10-6\sqrt{3}}{4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{3}}{2*2}=\frac{10+6\sqrt{3}}{4}
$