G=x^2-6x-12

Solution for G=x^2-6x-12 equation:

=G^2-6G-12

We move all terms to the left:

-(G^2-6G-12)=0

We get rid of parentheses

-G^2+6G+12=0

We add all the numbers together, and all the variables

-1G^2+6G+12=0

a = -1; b = 6; c = +12;
Δ = b2-4ac
Δ = 62-4·(-1)·12
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*-1}=\frac{-6-2\sqrt{21}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*-1}=\frac{-6+2\sqrt{21}}{-2}
$