G(x)=5x/3x-19

Solution for G(x)=5x/3x-19 equation:

(G)=5G/3G-19

We move all terms to the left:

(G)-(5G/3G-19)=0


Domain of the equation: 3G-19)!=0

G∈R


We get rid of parentheses

G-5G/3G+19=0

We multiply all the terms by the denominator


G*3G-5G+19*3G=0

We add all the numbers together, and all the variables

-5G+G*3G+19*3G=0

Wy multiply elements

3G^2-5G+57G=0

We add all the numbers together, and all the variables

3G^2+52G=0

a = 3; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·3·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*3}=\frac{-104}{6}
=-17+1/3
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*3}=\frac{0}{6}
=0
$