E=(-3x+4)(3x-8)-(-3x+4)(7x+2)

Solution for E=(-3x+4)(3x-8)-(-3x+4)(7x+2) equation:

=(-3E+4)(3E-8)-(-3E+4)(7E+2)

We move all terms to the left:

-((-3E+4)(3E-8)-(-3E+4)(7E+2))=0

We multiply parentheses ..

-((-9E^2+24E+12E-32)-(-3E+4)(7E+2))=0


We calculate terms in parentheses: -((-9E^2+24E+12E-32)-(-3E+4)(7E+2)), so:

(-9E^2+24E+12E-32)-(-3E+4)(7E+2)

We get rid of parentheses

-9E^2+24E+12E-(-3E+4)(7E+2)-32

We multiply parentheses ..

-9E^2-(-21E^2-6E+28E+8)+24E+12E-32

We add all the numbers together, and all the variables

-9E^2-(-21E^2-6E+28E+8)+36E-32

We get rid of parentheses

-9E^2+21E^2+6E-28E+36E-8-32

We add all the numbers together, and all the variables

12E^2+14E-40

Back to the equation:

-(12E^2+14E-40)


We get rid of parentheses

-12E^2-14E+40=0

a = -12; b = -14; c = +40;
Δ = b2-4ac
Δ = -142-4·(-12)·40
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-46}{2*-12}=\frac{-32}{-24}
=1+1/3
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+46}{2*-12}=\frac{60}{-24}
=-2+1/2
$