G(x)=-2/5x-2

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

(G)=-2/5G-2

We move all terms to the left:

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


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

G∈R


We get rid of parentheses

G+2/5G+2=0

We multiply all the terms by the denominator


G*5G+2*5G+2=0

Wy multiply elements

5G^2+10G+2=0

a = 5; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·5·2
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{15}}{2*5}=\frac{-10-2\sqrt{15}}{10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{15}}{2*5}=\frac{-10+2\sqrt{15}}{10}
$