G(x)=2x^2-10x+8

Solution for G(x)=2x^2-10x+8 equation:

(G)=2G^2-10G+8

We move all terms to the left:

(G)-(2G^2-10G+8)=0

We get rid of parentheses

-2G^2+G+10G-8=0

We add all the numbers together, and all the variables

-2G^2+11G-8=0

a = -2; b = 11; c = -8;
Δ = b2-4ac
Δ = 112-4·(-2)·(-8)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{57}}{2*-2}=\frac{-11-\sqrt{57}}{-4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{57}}{2*-2}=\frac{-11+\sqrt{57}}{-4}
$