G(x)=-8x2+3

Solution for G(x)=-8x2+3 equation:

(G)=-8G^2+3

We move all terms to the left:

(G)-(-8G^2+3)=0

We get rid of parentheses

8G^2+G-3=0

a = 8; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·8·(-3)
Δ = 97
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{-(1)-\sqrt{97}}{2*8}=\frac{-1-\sqrt{97}}{16}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*8}=\frac{-1+\sqrt{97}}{16}
$