5x=11/2x=10/11

Solution for 5x=11/2x=10/11 equation:

5x=11/2x=10/11

We move all terms to the left:

5x-(11/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+11/2x)=0

We get rid of parentheses

5x-11/2x=0

We multiply all the terms by the denominator


5x*2x-11=0

Wy multiply elements

10x^2-11=0

a = 10; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·10·(-11)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*10}=\frac{0-2\sqrt{110}}{20}
=-\frac{2\sqrt{110}}{20}
=-\frac{\sqrt{110}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*10}=\frac{0+2\sqrt{110}}{20}
=\frac{2\sqrt{110}}{20}
=\frac{\sqrt{110}}{10}
$