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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

(x+2)(x+2)

We multiply parentheses ..

(+x^2+2x+2x+4)

We get rid of parentheses

x^2+2x+2x+4

We add all the numbers together, and all the variables

x^2+4x+4

Back to the equation:

-(x^2+4x+4)


We multiply parentheses

4x^2-12x-4x-(x^2+4x+4)+12=0

We get rid of parentheses

4x^2-x^2-12x-4x-4x-4+12=0

We add all the numbers together, and all the variables

3x^2-20x+8=0

a = 3; b = -20; c = +8;
Δ = b2-4ac
Δ = -202-4·3·8
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{19}}{2*3}=\frac{20-4\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{19}}{2*3}=\frac{20+4\sqrt{19}}{6}
$