G(x)=2/5x-4

Solution for G(x)=2/5x-4 equation:

(G)=2/5G-4

We move all terms to the left:

(G)-(2/5G-4)=0


Domain of the equation: 5G-4)!=0

G∈R


We get rid of parentheses

G-2/5G+4=0

We multiply all the terms by the denominator


G*5G+4*5G-2=0

Wy multiply elements

5G^2+20G-2=0

a = 5; b = 20; c = -2;
Δ = b2-4ac
Δ = 202-4·5·(-2)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{110}}{2*5}=\frac{-20-2\sqrt{110}}{10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{110}}{2*5}=\frac{-20+2\sqrt{110}}{10}
$