G(x)=-3x^2+15x+72

Solution for G(x)=-3x^2+15x+72 equation:

(G)=-3G^2+15G+72

We move all terms to the left:

(G)-(-3G^2+15G+72)=0

We get rid of parentheses

3G^2-15G+G-72=0

We add all the numbers together, and all the variables

3G^2-14G-72=0

a = 3; b = -14; c = -72;
Δ = b2-4ac
Δ = -142-4·3·(-72)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{265}}{2*3}=\frac{14-2\sqrt{265}}{6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{265}}{2*3}=\frac{14+2\sqrt{265}}{6}
$