G(x)=-25+x^2

Solution for G(x)=-25+x^2 equation:

(G)=-25+G^2

We move all terms to the left:

(G)-(-25+G^2)=0

We get rid of parentheses

-G^2+G+25=0

We add all the numbers together, and all the variables

-1G^2+G+25=0

a = -1; b = 1; c = +25;
Δ = b2-4ac
Δ = 12-4·(-1)·25
Δ = 101
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{101}}{2*-1}=\frac{-1-\sqrt{101}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{101}}{2*-1}=\frac{-1+\sqrt{101}}{-2}
$