G=6x(2x+1)

Solution for G=6x(2x+1) equation:

=6G(2G+1)

We move all terms to the left:

-(6G(2G+1))=0


We calculate terms in parentheses: -(6G(2G+1)), so:

6G(2G+1)

We multiply parentheses

12G^2+6G

Back to the equation:

-(12G^2+6G)


We get rid of parentheses

-12G^2-6G=0

a = -12; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-12)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-12}=\frac{0}{-24}
=0
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-12}=\frac{12}{-24}
=-1/2
$