G(x)=1/4x+6

Solution for G(x)=1/4x+6 equation:

(G)=1/4G+6

We move all terms to the left:

(G)-(1/4G+6)=0


Domain of the equation: 4G+6)!=0

G∈R


We get rid of parentheses

G-1/4G-6=0

We multiply all the terms by the denominator


G*4G-6*4G-1=0

Wy multiply elements

4G^2-24G-1=0

a = 4; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·4·(-1)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{37}}{2*4}=\frac{24-4\sqrt{37}}{8}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{37}}{2*4}=\frac{24+4\sqrt{37}}{8}
$