E(7)=-x^2-9x

Solution for E(7)=-x^2-9x equation:

(7)=-E^2-9E

We move all terms to the left:

(7)-(-E^2-9E)=0

We get rid of parentheses

E^2+9E+7=0

a = 1; b = 9; c = +7;
Δ = b2-4ac
Δ = 92-4·1·7
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{53}}{2*1}=\frac{-9-\sqrt{53}}{2}
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{53}}{2*1}=\frac{-9+\sqrt{53}}{2}
$