G(x)=3x^2-18x+15

Solution for G(x)=3x^2-18x+15 equation:

(G)=3G^2-18G+15

We move all terms to the left:

(G)-(3G^2-18G+15)=0

We get rid of parentheses

-3G^2+G+18G-15=0

We add all the numbers together, and all the variables

-3G^2+19G-15=0

a = -3; b = 19; c = -15;
Δ = b2-4ac
Δ = 192-4·(-3)·(-15)
Δ = 181
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{-(19)-\sqrt{181}}{2*-3}=\frac{-19-\sqrt{181}}{-6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{181}}{2*-3}=\frac{-19+\sqrt{181}}{-6}
$