2x+11/2x-20=101/2x

Solution for 2x+11/2x-20=101/2x equation:

2x+11/2x-20=101/2x

We move all terms to the left:

2x+11/2x-20-(101/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+11/2x-(+101/2x)-20=0

We get rid of parentheses

2x+11/2x-101/2x-20=0

We multiply all the terms by the denominator


2x*2x-20*2x+11-101=0

We add all the numbers together, and all the variables

2x*2x-20*2x-90=0

Wy multiply elements

4x^2-40x-90=0

a = 4; b = -40; c = -90;
Δ = b2-4ac
Δ = -402-4·4·(-90)
Δ = 3040
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:

$\sqrt{\Delta}=\sqrt{3040}=\sqrt{16*190}=\sqrt{16}*\sqrt{190}=4\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{190}}{2*4}=\frac{40-4\sqrt{190}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{190}}{2*4}=\frac{40+4\sqrt{190}}{8}
$