4*(x+1)*(x+1)=(3x-122)*(3x-122)

Solution for 4*(x+1)*(x+1)=(3x-122)*(3x-122) equation:

4(x+1)(x+1)=(3x-122)(3x-122)

We move all terms to the left:

4(x+1)(x+1)-((3x-122)(3x-122))=0

We multiply parentheses ..

4(+x^2+x+x+1)-((3x-122)(3x-122))=0


We calculate terms in parentheses: -((3x-122)(3x-122)), so:

(3x-122)(3x-122)

We multiply parentheses ..

(+9x^2-366x-366x+14884)

We get rid of parentheses

9x^2-366x-366x+14884

We add all the numbers together, and all the variables

9x^2-732x+14884

Back to the equation:

-(9x^2-732x+14884)


We multiply parentheses

4x^2+4x+4x-(9x^2-732x+14884)+4=0

We get rid of parentheses

4x^2-9x^2+4x+4x+732x-14884+4=0

We add all the numbers together, and all the variables

-5x^2+740x-14880=0

a = -5; b = 740; c = -14880;
Δ = b2-4ac
Δ = 7402-4·(-5)·(-14880)
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(740)-500}{2*-5}=\frac{-1240}{-10}
=+124
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(740)+500}{2*-5}=\frac{-240}{-10}
=+24
$