G(x)=3x2+-8x

Solution for G(x)=3x2+-8x equation:

(G)=3G^2+-8G

We move all terms to the left:

(G)-(3G^2+-8G)=0

We use the square of the difference formula

G-(3G^2-8G)=0

We get rid of parentheses

-3G^2+G+8G=0

We add all the numbers together, and all the variables

-3G^2+9G=0

a = -3; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-3)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-3}=\frac{-18}{-6}
=+3
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-3}=\frac{0}{-6}
=0
$