2x+4/4x-88=180

Solution for 2x+4/4x-88=180 equation:

2x+4/4x-88=180

We move all terms to the left:

2x+4/4x-88-(180)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+4/4x-268=0

We multiply all the terms by the denominator


2x*4x-268*4x+4=0

Wy multiply elements

8x^2-1072x+4=0

a = 8; b = -1072; c = +4;
Δ = b2-4ac
Δ = -10722-4·8·4
Δ = 1149056
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:

$\sqrt{\Delta}=\sqrt{1149056}=\sqrt{64*17954}=\sqrt{64}*\sqrt{17954}=8\sqrt{17954}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1072)-8\sqrt{17954}}{2*8}=\frac{1072-8\sqrt{17954}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1072)+8\sqrt{17954}}{2*8}=\frac{1072+8\sqrt{17954}}{16}
$