G(x)=-x2-6x+31

Solution for G(x)=-x2-6x+31 equation:

(G)=-G2-6G+31

We move all terms to the left:

(G)-(-G2-6G+31)=0

We add all the numbers together, and all the variables

-(-1G^2-6G+31)+G=0

We get rid of parentheses

1G^2+6G+G-31=0

We add all the numbers together, and all the variables

G^2+7G-31=0

a = 1; b = 7; c = -31;
Δ = b2-4ac
Δ = 72-4·1·(-31)
Δ = 173
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{-(7)-\sqrt{173}}{2*1}=\frac{-7-\sqrt{173}}{2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{173}}{2*1}=\frac{-7+\sqrt{173}}{2}
$