2x+11/2x-20=10+1/2x

Solution for 2x+11/2x-20=10+1/2x equation:

2x+11/2x-20=10+1/2x

We move all terms to the left:

2x+11/2x-20-(10+1/2x)=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-(1/2x+10)-20=0

We get rid of parentheses

2x+11/2x-1/2x-10-20=0

We multiply all the terms by the denominator


2x*2x-10*2x-20*2x+11-1=0

We add all the numbers together, and all the variables

2x*2x-10*2x-20*2x+10=0

Wy multiply elements

4x^2-20x-40x+10=0

We add all the numbers together, and all the variables

4x^2-60x+10=0

a = 4; b = -60; c = +10;
Δ = b2-4ac
Δ = -602-4·4·10
Δ = 3440
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:

$\sqrt{\Delta}=\sqrt{3440}=\sqrt{16*215}=\sqrt{16}*\sqrt{215}=4\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{215}}{2*4}=\frac{60-4\sqrt{215}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{215}}{2*4}=\frac{60+4\sqrt{215}}{8}
$