G(x)=3x^2+14x-5

Solution for G(x)=3x^2+14x-5 equation:

(G)=3G^2+14G-5

We move all terms to the left:

(G)-(3G^2+14G-5)=0

We get rid of parentheses

-3G^2+G-14G+5=0

We add all the numbers together, and all the variables

-3G^2-13G+5=0

a = -3; b = -13; c = +5;
Δ = b2-4ac
Δ = -132-4·(-3)·5
Δ = 229
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{-(-13)-\sqrt{229}}{2*-3}=\frac{13-\sqrt{229}}{-6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{229}}{2*-3}=\frac{13+\sqrt{229}}{-6}
$