G(x)=2(3x)2-3(3x)+5

Solution for G(x)=2(3x)2-3(3x)+5 equation:

(G)=2(3G)2-3(3G)+5

We move all terms to the left:

(G)-(2(3G)2-3(3G)+5)=0

We add all the numbers together, and all the variables

-(+23G^2-33G+5)+G=0

We get rid of parentheses

-23G^2+33G+G-5=0

We add all the numbers together, and all the variables

-23G^2+34G-5=0

a = -23; b = 34; c = -5;
Δ = b2-4ac
Δ = 342-4·(-23)·(-5)
Δ = 696
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:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{174}}{2*-23}=\frac{-34-2\sqrt{174}}{-46}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{174}}{2*-23}=\frac{-34+2\sqrt{174}}{-46}
$