G(X)=3x2+-4x+-1

Solution for G(X)=3x2+-4x+-1 equation:

(G)=3G^2+-4G+-1

We move all terms to the left:

(G)-(3G^2+-4G+-1)=0

We use the square of the difference formula

G-(3G^2-4G-1)=0

We get rid of parentheses

-3G^2+G+4G+1=0

We add all the numbers together, and all the variables

-3G^2+5G+1=0

a = -3; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·(-3)·1
Δ = 37
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{-(5)-\sqrt{37}}{2*-3}=\frac{-5-\sqrt{37}}{-6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*-3}=\frac{-5+\sqrt{37}}{-6}
$