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+15G+5=0

a = -3; b = 15; c = +5;
Δ = b2-4ac
Δ = 152-4·(-3)·5
Δ = 285
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{-(15)-\sqrt{285}}{2*-3}=\frac{-15-\sqrt{285}}{-6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{285}}{2*-3}=\frac{-15+\sqrt{285}}{-6}
$