2x+4/4x=20

Solution for 2x+4/4x=20 equation:

2x+4/4x=20

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-80x+4=0

a = 8; b = -80; c = +4;
Δ = b2-4ac
Δ = -802-4·8·4
Δ = 6272
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:

$\sqrt{\Delta}=\sqrt{6272}=\sqrt{3136*2}=\sqrt{3136}*\sqrt{2}=56\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-56\sqrt{2}}{2*8}=\frac{80-56\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+56\sqrt{2}}{2*8}=\frac{80+56\sqrt{2}}{16}
$