G(x)=-3x^2+18x-5

Solution for G(x)=-3x^2+18x-5 equation:

(G)=-3G^2+18G-5

We move all terms to the left:

(G)-(-3G^2+18G-5)=0

We get rid of parentheses

3G^2-18G+G+5=0

We add all the numbers together, and all the variables

3G^2-17G+5=0

a = 3; b = -17; c = +5;
Δ = b2-4ac
Δ = -172-4·3·5
Δ = 229
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{-(-17)-\sqrt{229}}{2*3}=\frac{17-\sqrt{229}}{6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{229}}{2*3}=\frac{17+\sqrt{229}}{6}
$