G(x)=5x^2-8

Solution for G(x)=5x^2-8 equation:

(G)=5G^2-8

We move all terms to the left:

(G)-(5G^2-8)=0

We get rid of parentheses

-5G^2+G+8=0

a = -5; b = 1; c = +8;
Δ = b2-4ac
Δ = 12-4·(-5)·8
Δ = 161
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{161}}{2*-5}=\frac{-1-\sqrt{161}}{-10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{161}}{2*-5}=\frac{-1+\sqrt{161}}{-10}
$