E=225z2-64+(-15z+8)(6z+12)

Solution for E=225z2-64+(-15z+8)(6z+12) equation:

=225E^2-64+(-15E+8)(6E+12)

We move all terms to the left:

-(225E^2-64+(-15E+8)(6E+12))=0

We multiply parentheses ..

-(225E^2-64+(-90E^2-180E+48E+96))=0


We calculate terms in parentheses: -(225E^2-64+(-90E^2-180E+48E+96)), so:

225E^2-64+(-90E^2-180E+48E+96)

determiningTheFunctionDomain
225E^2+(-90E^2-180E+48E+96)-64

We get rid of parentheses

225E^2-90E^2-180E+48E+96-64

We add all the numbers together, and all the variables

135E^2-132E+32

Back to the equation:

-(135E^2-132E+32)


We get rid of parentheses

-135E^2+132E-32=0

a = -135; b = 132; c = -32;
Δ = b2-4ac
Δ = 1322-4·(-135)·(-32)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-12}{2*-135}=\frac{-144}{-270}
=8/15
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+12}{2*-135}=\frac{-120}{-270}
=4/9
$