G(x)=20/x-3

Solution for G(x)=20/x-3 equation:

(G)=20/G-3

We move all terms to the left:

(G)-(20/G-3)=0


Domain of the equation: G-3)!=0

G∈R


We get rid of parentheses

G-20/G+3=0

We multiply all the terms by the denominator


G*G+3*G-20=0

We add all the numbers together, and all the variables

3G+G*G-20=0

Wy multiply elements

G^2+3G-20=0

a = 1; b = 3; c = -20;
Δ = b2-4ac
Δ = 32-4·1·(-20)
Δ = 89
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{-(3)-\sqrt{89}}{2*1}=\frac{-3-\sqrt{89}}{2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{89}}{2*1}=\frac{-3+\sqrt{89}}{2}
$