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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

5(5x-3)(5x-3)

We multiply parentheses ..

5(+25x^2-15x-15x+9)

We multiply parentheses

125x^2-75x-75x+45

We add all the numbers together, and all the variables

125x^2-150x+45

Back to the equation:

-(125x^2-150x+45)


We multiply parentheses

3x^2+3x+3x-(125x^2-150x+45)+3=0

We get rid of parentheses

3x^2-125x^2+3x+3x+150x-45+3=0

We add all the numbers together, and all the variables

-122x^2+156x-42=0

a = -122; b = 156; c = -42;
Δ = b2-4ac
Δ = 1562-4·(-122)·(-42)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-16\sqrt{15}}{2*-122}=\frac{-156-16\sqrt{15}}{-244}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+16\sqrt{15}}{2*-122}=\frac{-156+16\sqrt{15}}{-244}
$