G(x)=-6(x-2)(x)

Solution for G(x)=-6(x-2)(x) equation:

(G)=-6(G-2)(G)

We move all terms to the left:

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


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

-6(G-2)G

We multiply parentheses

-6G^2+12G

Back to the equation:

-(-6G^2+12G)


We get rid of parentheses

6G^2-12G+G=0

We add all the numbers together, and all the variables

6G^2-11G=0

a = 6; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·6·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*6}=\frac{0}{12}
=0
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*6}=\frac{22}{12}
=1+5/6
$