2x+4+50/x=4x+4

Solution for 2x+4+50/x=4x+4 equation:

2x+4+50/x=4x+4

We move all terms to the left:

2x+4+50/x-(4x+4)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2x+50/x-4x-4+4=0

We multiply all the terms by the denominator


2x*x-4x*x-4*x+4*x+50=0

We add all the numbers together, and all the variables

2x*x-4x*x+50=0

Wy multiply elements

2x^2-4x^2+50=0

We add all the numbers together, and all the variables

-2x^2+50=0

a = -2; b = 0; c = +50;
Δ = b2-4ac
Δ = 02-4·(-2)·50
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*-2}=\frac{20}{-4}
=-5
$