G(x)=-2x^2+4x+6

Solution for G(x)=-2x^2+4x+6 equation:

(G)=-2G^2+4G+6

We move all terms to the left:

(G)-(-2G^2+4G+6)=0

We get rid of parentheses

2G^2-4G+G-6=0

We add all the numbers together, and all the variables

2G^2-3G-6=0

a = 2; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·2·(-6)
Δ = 57
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{-(-3)-\sqrt{57}}{2*2}=\frac{3-\sqrt{57}}{4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*2}=\frac{3+\sqrt{57}}{4}
$