E=(3x-1)(7x+9)

Solution for E=(3x-1)(7x+9) equation:

=(3E-1)(7E+9)

We move all terms to the left:

-((3E-1)(7E+9))=0

We multiply parentheses ..

-((+21E^2+27E-7E-9))=0


We calculate terms in parentheses: -((+21E^2+27E-7E-9)), so:

(+21E^2+27E-7E-9)

We get rid of parentheses

21E^2+27E-7E-9

We add all the numbers together, and all the variables

21E^2+20E-9

Back to the equation:

-(21E^2+20E-9)


We get rid of parentheses

-21E^2-20E+9=0

a = -21; b = -20; c = +9;
Δ = b2-4ac
Δ = -202-4·(-21)·9
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-34}{2*-21}=\frac{-14}{-42}
=1/3
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+34}{2*-21}=\frac{54}{-42}
=-1+2/7
$