4x(x+1)=4x+16x

Solution for 4x(x+1)=4x+16x equation:

4x(x+1)=4x+16x

We move all terms to the left:

4x(x+1)-(4x+16x)=0

We add all the numbers together, and all the variables

4x(x+1)-(+20x)=0

We multiply parentheses

4x^2+4x-(+20x)=0

We get rid of parentheses

4x^2+4x-20x=0

We add all the numbers together, and all the variables

4x^2-16x=0

a = 4; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·4·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*4}=\frac{32}{8}
=4
$