E=(x-6)(x+5)+(x+2)(x-1)

Solution for E=(x-6)(x+5)+(x+2)(x-1) equation:

=(E-6)(E+5)+(E+2)(E-1)

We move all terms to the left:

-((E-6)(E+5)+(E+2)(E-1))=0

We multiply parentheses ..

-((+E^2+5E-6E-30)+(E+2)(E-1))=0


We calculate terms in parentheses: -((+E^2+5E-6E-30)+(E+2)(E-1)), so:

(+E^2+5E-6E-30)+(E+2)(E-1)

We get rid of parentheses

E^2+5E-6E+(E+2)(E-1)-30

We multiply parentheses ..

E^2+(+E^2-1E+2E-2)+5E-6E-30

We add all the numbers together, and all the variables

E^2+(+E^2-1E+2E-2)-1E-30

We get rid of parentheses

E^2+E^2-1E+2E-1E-2-30

We add all the numbers together, and all the variables

2E^2-32

Back to the equation:

-(2E^2-32)


We get rid of parentheses

-2E^2+32=0

a = -2; b = 0; c = +32;
Δ = b2-4ac
Δ = 02-4·(-2)·32
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*-2}=\frac{-16}{-4}
=+4
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*-2}=\frac{16}{-4}
=-4
$