E=(3x-7)(3x-7)-(5x-1)(5x-3)

Solution for E=(3x-7)(3x-7)-(5x-1)(5x-3) equation:

=(3E-7)(3E-7)-(5E-1)(5E-3)

We move all terms to the left:

-((3E-7)(3E-7)-(5E-1)(5E-3))=0

We multiply parentheses ..

-((+9E^2-21E-21E+49)-(5E-1)(5E-3))=0


We calculate terms in parentheses: -((+9E^2-21E-21E+49)-(5E-1)(5E-3)), so:

(+9E^2-21E-21E+49)-(5E-1)(5E-3)

We get rid of parentheses

9E^2-21E-21E-(5E-1)(5E-3)+49

We multiply parentheses ..

9E^2-(+25E^2-15E-5E+3)-21E-21E+49

We add all the numbers together, and all the variables

9E^2-(+25E^2-15E-5E+3)-42E+49

We get rid of parentheses

9E^2-25E^2+15E+5E-42E-3+49

We add all the numbers together, and all the variables

-16E^2-22E+46

Back to the equation:

-(-16E^2-22E+46)


We get rid of parentheses

16E^2+22E-46=0

a = 16; b = 22; c = -46;
Δ = b2-4ac
Δ = 222-4·16·(-46)
Δ = 3428
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3428}=\sqrt{4*857}=\sqrt{4}*\sqrt{857}=2\sqrt{857}$
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{857}}{2*16}=\frac{-22-2\sqrt{857}}{32}
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{857}}{2*16}=\frac{-22+2\sqrt{857}}{32}
$