x+4x(x+55)=x

Solution for x+4x(x+55)=x equation:

x+4x(x+55)=x

We move all terms to the left:

x+4x(x+55)-(x)=0

We add all the numbers together, and all the variables

4x(x+55)=0

We multiply parentheses

4x^2+220x=0

a = 4; b = 220; c = 0;
Δ = b2-4ac
Δ = 2202-4·4·0
Δ = 48400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{48400}=220$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-220}{2*4}=\frac{-440}{8}
=-55
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+220}{2*4}=\frac{0}{8}
=0
$