(x+7)(x+7)=(x+7)(3x+5)

Solution for (x+7)(x+7)=(x+7)(3x+5) equation:

(x+7)(x+7)=(x+7)(3x+5)

We move all terms to the left:

(x+7)(x+7)-((x+7)(3x+5))=0

We multiply parentheses ..

(+x^2+7x+7x+49)-((x+7)(3x+5))=0


We calculate terms in parentheses: -((x+7)(3x+5)), so:

(x+7)(3x+5)

We multiply parentheses ..

(+3x^2+5x+21x+35)

We get rid of parentheses

3x^2+5x+21x+35

We add all the numbers together, and all the variables

3x^2+26x+35

Back to the equation:

-(3x^2+26x+35)


We get rid of parentheses

x^2-3x^2+7x+7x-26x+49-35=0

We add all the numbers together, and all the variables

-2x^2-12x+14=0

a = -2; b = -12; c = +14;
Δ = b2-4ac
Δ = -122-4·(-2)·14
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16}{2*-2}=\frac{28}{-4}
=-7
$