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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

3(x-5)(x-5)

We multiply parentheses ..

3(+x^2-5x-5x+25)

We multiply parentheses

3x^2-15x-15x+75

We add all the numbers together, and all the variables

3x^2-30x+75

Back to the equation:

-(3x^2-30x+75)


We get rid of parentheses

x^2-3x^2+7x+7x+30x+49-75=0

We add all the numbers together, and all the variables

-2x^2+44x-26=0

a = -2; b = 44; c = -26;
Δ = b2-4ac
Δ = 442-4·(-2)·(-26)
Δ = 1728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-24\sqrt{3}}{2*-2}=\frac{-44-24\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+24\sqrt{3}}{2*-2}=\frac{-44+24\sqrt{3}}{-4}
$