2x+2x+31/4x+1=65

Solution for 2x+2x+31/4x+1=65 equation:

2x+2x+31/4x+1=65

We move all terms to the left:

2x+2x+31/4x+1-(65)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

4x+31/4x-64=0

We multiply all the terms by the denominator


4x*4x-64*4x+31=0

Wy multiply elements

16x^2-256x+31=0

a = 16; b = -256; c = +31;
Δ = b2-4ac
Δ = -2562-4·16·31
Δ = 63552
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:

$\sqrt{\Delta}=\sqrt{63552}=\sqrt{64*993}=\sqrt{64}*\sqrt{993}=8\sqrt{993}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-256)-8\sqrt{993}}{2*16}=\frac{256-8\sqrt{993}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-256)+8\sqrt{993}}{2*16}=\frac{256+8\sqrt{993}}{32}
$