G(x)=5x2-4x

Solution for G(x)=5x2-4x equation:

(G)=5G^2-4G

We move all terms to the left:

(G)-(5G^2-4G)=0

We get rid of parentheses

-5G^2+G+4G=0

We add all the numbers together, and all the variables

-5G^2+5G=0

a = -5; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-5)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-5}=\frac{-10}{-10}
=1
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-5}=\frac{0}{-10}
=0
$