2/4x+2x=130

Solution for 2/4x+2x=130 equation:

2/4x+2x=130

We move all terms to the left:

2/4x+2x-(130)=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+2/4x-130=0

We multiply all the terms by the denominator


2x*4x-130*4x+2=0

Wy multiply elements

8x^2-520x+2=0

a = 8; b = -520; c = +2;
Δ = b2-4ac
Δ = -5202-4·8·2
Δ = 270336
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:

$\sqrt{\Delta}=\sqrt{270336}=\sqrt{4096*66}=\sqrt{4096}*\sqrt{66}=64\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-520)-64\sqrt{66}}{2*8}=\frac{520-64\sqrt{66}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-520)+64\sqrt{66}}{2*8}=\frac{520+64\sqrt{66}}{16}
$