G(x)=-9/5x-8

Solution for G(x)=-9/5x-8 equation:

(G)=-9/5G-8

We move all terms to the left:

(G)-(-9/5G-8)=0


Domain of the equation: 5G-8)!=0

G∈R


We get rid of parentheses

G+9/5G+8=0

We multiply all the terms by the denominator


G*5G+8*5G+9=0

Wy multiply elements

5G^2+40G+9=0

a = 5; b = 40; c = +9;
Δ = b2-4ac
Δ = 402-4·5·9
Δ = 1420
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:

$\sqrt{\Delta}=\sqrt{1420}=\sqrt{4*355}=\sqrt{4}*\sqrt{355}=2\sqrt{355}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{355}}{2*5}=\frac{-40-2\sqrt{355}}{10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{355}}{2*5}=\frac{-40+2\sqrt{355}}{10}
$