E(x)=-10x2+120x

Solution for E(x)=-10x2+120x equation:

(E)=-10E^2+120E

We move all terms to the left:

(E)-(-10E^2+120E)=0

We get rid of parentheses

10E^2-120E+E=0

We add all the numbers together, and all the variables

10E^2-119E=0

a = 10; b = -119; c = 0;
Δ = b2-4ac
Δ = -1192-4·10·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-119}{2*10}=\frac{0}{20}
=0
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+119}{2*10}=\frac{238}{20}
=11+9/10
$