G(x)=x^2/8-3

Solution for G(x)=x^2/8-3 equation:

(G)=G^2/8-3

We move all terms to the left:

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

We get rid of parentheses

-G^2/8+G+3=0

We multiply all the terms by the denominator


-G^2+G*8+3*8=0

We add all the numbers together, and all the variables

-1G^2+G*8+24=0

Wy multiply elements

-1G^2+8G+24=0

a = -1; b = 8; c = +24;
Δ = b2-4ac
Δ = 82-4·(-1)·24
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*-1}=\frac{-8-4\sqrt{10}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*-1}=\frac{-8+4\sqrt{10}}{-2}
$