2x+2/4x=80

Solution for 2x+2/4x=80 equation:

2x+2/4x=80

We move all terms to the left:

2x+2/4x-(80)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-80*4x+2=0

Wy multiply elements

8x^2-320x+2=0

a = 8; b = -320; c = +2;
Δ = b2-4ac
Δ = -3202-4·8·2
Δ = 102336
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:

$\sqrt{\Delta}=\sqrt{102336}=\sqrt{64*1599}=\sqrt{64}*\sqrt{1599}=8\sqrt{1599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-8\sqrt{1599}}{2*8}=\frac{320-8\sqrt{1599}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+8\sqrt{1599}}{2*8}=\frac{320+8\sqrt{1599}}{16}
$