G(w)=6w^2-14w-3

Solution for G(w)=6w^2-14w-3 equation:

(G)=6G^2-14G-3

We move all terms to the left:

(G)-(6G^2-14G-3)=0

We get rid of parentheses

-6G^2+G+14G+3=0

We add all the numbers together, and all the variables

-6G^2+15G+3=0

a = -6; b = 15; c = +3;
Δ = b2-4ac
Δ = 152-4·(-6)·3
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{33}}{2*-6}=\frac{-15-3\sqrt{33}}{-12}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{33}}{2*-6}=\frac{-15+3\sqrt{33}}{-12}
$