(3-4x)(3+4x)=3(3x-2)(x+1)-(5x-3)(5x+3)

Solution for (3-4x)(3+4x)=3(3x-2)(x+1)-(5x-3)(5x+3) equation:

(3-4x)(3+4x)=3(3x-2)(x+1)-(5x-3)(5x+3)

We move all terms to the left:

(3-4x)(3+4x)-(3(3x-2)(x+1)-(5x-3)(5x+3))=0

We add all the numbers together, and all the variables

(-4x+3)(4x+3)-(3(3x-2)(x+1)-(5x-3)(5x+3))=0

We multiply parentheses ..

(-16x^2-12x+12x+9)-(3(3x-2)(x+1)-(5x-3)(5x+3))=0


We calculate terms in parentheses: -(3(3x-2)(x+1)-(5x-3)(5x+3)), so:

3(3x-2)(x+1)-(5x-3)(5x+3)

We use the square of the difference formula

25x^2+3(3x-2)(x+1)+9

We multiply parentheses ..

25x^2+3(+3x^2+3x-2x-2)+9

We multiply parentheses

25x^2+9x^2+9x-6x-6+9

We add all the numbers together, and all the variables

34x^2+3x+3

Back to the equation:

-(34x^2+3x+3)


We get rid of parentheses

-16x^2-34x^2-12x+12x-3x+9-3=0

We add all the numbers together, and all the variables

-50x^2-3x+6=0

a = -50; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-50)·6
Δ = 1209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{1209}}{2*-50}=\frac{3-\sqrt{1209}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1209}}{2*-50}=\frac{3+\sqrt{1209}}{-100}
$