G(x)=-3x2-7x+6

Solution for G(x)=-3x2-7x+6 equation:

(G)=-3G^2-7G+6

We move all terms to the left:

(G)-(-3G^2-7G+6)=0

We get rid of parentheses

3G^2+7G+G-6=0

We add all the numbers together, and all the variables

3G^2+8G-6=0

a = 3; b = 8; c = -6;
Δ = b2-4ac
Δ = 82-4·3·(-6)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{34}}{2*3}=\frac{-8-2\sqrt{34}}{6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{34}}{2*3}=\frac{-8+2\sqrt{34}}{6}
$