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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(4(-1x+2)), so:

4(-1x+2)

We multiply parentheses

-4x+8

Back to the equation:

-(-4x+8)


We get rid of parentheses

4x^2+4x+4x-8=0

We add all the numbers together, and all the variables

4x^2+8x-8=0

a = 4; b = 8; c = -8;
Δ = b2-4ac
Δ = 82-4·4·(-8)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{3}}{2*4}=\frac{-8-8\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{3}}{2*4}=\frac{-8+8\sqrt{3}}{8}
$