E=6x(2+9x)

Solution for E=6x(2+9x) equation:

=6E(2+9E)

We move all terms to the left:

-(6E(2+9E))=0

We add all the numbers together, and all the variables

-(6E(9E+2))=0


We calculate terms in parentheses: -(6E(9E+2)), so:

6E(9E+2)

We multiply parentheses

54E^2+12E

Back to the equation:

-(54E^2+12E)


We get rid of parentheses

-54E^2-12E=0

a = -54; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-54)·0
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{-(-12)-12}{2*-54}=\frac{0}{-108}
=0
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-54}=\frac{24}{-108}
=-2/9
$