G(x)=3/5x-9

Solution for G(x)=3/5x-9 equation:

(G)=3/5G-9

We move all terms to the left:

(G)-(3/5G-9)=0


Domain of the equation: 5G-9)!=0

G∈R


We get rid of parentheses

G-3/5G+9=0

We multiply all the terms by the denominator


G*5G+9*5G-3=0

Wy multiply elements

5G^2+45G-3=0

a = 5; b = 45; c = -3;
Δ = b2-4ac
Δ = 452-4·5·(-3)
Δ = 2085
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2085}}{2*5}=\frac{-45-\sqrt{2085}}{10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2085}}{2*5}=\frac{-45+\sqrt{2085}}{10}
$