2x+11/2x-20=1012x

Solution for 2x+11/2x-20=1012x equation:

2x+11/2x-20=1012x

We move all terms to the left:

2x+11/2x-20-(1012x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1010x+11/2x-20=0

We multiply all the terms by the denominator


-1010x*2x-20*2x+11=0

Wy multiply elements

-2020x^2-40x+11=0

a = -2020; b = -40; c = +11;
Δ = b2-4ac
Δ = -402-4·(-2020)·11
Δ = 90480
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:

$\sqrt{\Delta}=\sqrt{90480}=\sqrt{16*5655}=\sqrt{16}*\sqrt{5655}=4\sqrt{5655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{5655}}{2*-2020}=\frac{40-4\sqrt{5655}}{-4040}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{5655}}{2*-2020}=\frac{40+4\sqrt{5655}}{-4040}
$