G(X)=-16x^2+120x

Solution for G(X)=-16x^2+120x equation:

(G)=-16G^2+120G

We move all terms to the left:

(G)-(-16G^2+120G)=0

We get rid of parentheses

16G^2-120G+G=0

We add all the numbers together, and all the variables

16G^2-119G=0

a = 16; b = -119; c = 0;
Δ = b2-4ac
Δ = -1192-4·16·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-119}{2*16}=\frac{0}{32}
=0
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+119}{2*16}=\frac{238}{32}
=7+7/16
$