G(x)=-x2-x+7

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

(G)=-G2-G+7

We move all terms to the left:

(G)-(-G2-G+7)=0

We add all the numbers together, and all the variables

-(-1G^2-1G+7)+G=0

We get rid of parentheses

1G^2+1G+G-7=0

We add all the numbers together, and all the variables

G^2+2G-7=0

a = 1; b = 2; c = -7;
Δ = b2-4ac
Δ = 22-4·1·(-7)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{2}}{2*1}=\frac{-2-4\sqrt{2}}{2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{2}}{2*1}=\frac{-2+4\sqrt{2}}{2}
$