G(x)=-1/5x+6

Solution for G(x)=-1/5x+6 equation:

(G)=-1/5G+6

We move all terms to the left:

(G)-(-1/5G+6)=0


Domain of the equation: 5G+6)!=0

G∈R


We get rid of parentheses

G+1/5G-6=0

We multiply all the terms by the denominator


G*5G-6*5G+1=0

Wy multiply elements

5G^2-30G+1=0

a = 5; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·5·1
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{55}}{2*5}=\frac{30-4\sqrt{55}}{10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{55}}{2*5}=\frac{30+4\sqrt{55}}{10}
$