G(x)=7/3x-18

Solution for G(x)=7/3x-18 equation:

(G)=7/3G-18

We move all terms to the left:

(G)-(7/3G-18)=0


Domain of the equation: 3G-18)!=0

G∈R


We get rid of parentheses

G-7/3G+18=0

We multiply all the terms by the denominator


G*3G+18*3G-7=0

Wy multiply elements

3G^2+54G-7=0

a = 3; b = 54; c = -7;
Δ = b2-4ac
Δ = 542-4·3·(-7)
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-10\sqrt{30}}{2*3}=\frac{-54-10\sqrt{30}}{6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+10\sqrt{30}}{2*3}=\frac{-54+10\sqrt{30}}{6}
$