E(x)=4x^2-12x-21

Solution for E(x)=4x^2-12x-21 equation:

(E)=4E^2-12E-21

We move all terms to the left:

(E)-(4E^2-12E-21)=0

We get rid of parentheses

-4E^2+E+12E+21=0

We add all the numbers together, and all the variables

-4E^2+13E+21=0

a = -4; b = 13; c = +21;
Δ = b2-4ac
Δ = 132-4·(-4)·21
Δ = 505
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{-(13)-\sqrt{505}}{2*-4}=\frac{-13-\sqrt{505}}{-8}
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{505}}{2*-4}=\frac{-13+\sqrt{505}}{-8}
$