110/4x+2x=360

Solution for 110/4x+2x=360 equation:

110/4x+2x=360

We move all terms to the left:

110/4x+2x-(360)=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+110/4x-360=0

We multiply all the terms by the denominator


2x*4x-360*4x+110=0

Wy multiply elements

8x^2-1440x+110=0

a = 8; b = -1440; c = +110;
Δ = b2-4ac
Δ = -14402-4·8·110
Δ = 2070080
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:

$\sqrt{\Delta}=\sqrt{2070080}=\sqrt{64*32345}=\sqrt{64}*\sqrt{32345}=8\sqrt{32345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1440)-8\sqrt{32345}}{2*8}=\frac{1440-8\sqrt{32345}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1440)+8\sqrt{32345}}{2*8}=\frac{1440+8\sqrt{32345}}{16}
$