G(x)=X^2-4x-21

Solution for G(x)=X^2-4x-21 equation:

(G)=G^2-4G-21

We move all terms to the left:

(G)-(G^2-4G-21)=0

We get rid of parentheses

-G^2+G+4G+21=0

We add all the numbers together, and all the variables

-1G^2+5G+21=0

a = -1; b = 5; c = +21;
Δ = b2-4ac
Δ = 52-4·(-1)·21
Δ = 109
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{-(5)-\sqrt{109}}{2*-1}=\frac{-5-\sqrt{109}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{109}}{2*-1}=\frac{-5+\sqrt{109}}{-2}
$