G(x)=8(4x^2)-1

Solution for G(x)=8(4x^2)-1 equation:

(G)=8(4G^2)-1

We move all terms to the left:

(G)-(8(4G^2)-1)=0

We get rid of parentheses

-84G^2+G+1=0

a = -84; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-84)·1
Δ = 337
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{337}}{2*-84}=\frac{-1-\sqrt{337}}{-168}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{337}}{2*-84}=\frac{-1+\sqrt{337}}{-168}
$