G(x)=5x^2-6x+1

Solution for G(x)=5x^2-6x+1 equation:

(G)=5G^2-6G+1

We move all terms to the left:

(G)-(5G^2-6G+1)=0

We get rid of parentheses

-5G^2+G+6G-1=0

We add all the numbers together, and all the variables

-5G^2+7G-1=0

a = -5; b = 7; c = -1;
Δ = b2-4ac
Δ = 72-4·(-5)·(-1)
Δ = 29
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{-(7)-\sqrt{29}}{2*-5}=\frac{-7-\sqrt{29}}{-10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{29}}{2*-5}=\frac{-7+\sqrt{29}}{-10}
$