6/11-1/2x=3/22x-1

Solution for 6/11-1/2x=3/22x-1 equation:

6/11-1/2x=3/22x-1

We move all terms to the left:

6/11-1/2x-(3/22x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 22x-1)!=0

x∈R


We get rid of parentheses

-1/2x-3/22x+1+6/11=0

We calculate fractions


528x^2/484x^2+(-242x)/484x^2+(-66x)/484x^2+1=0

We multiply all the terms by the denominator


528x^2+(-242x)+(-66x)+1*484x^2=0

Wy multiply elements

528x^2+484x^2+(-242x)+(-66x)=0

We get rid of parentheses

528x^2+484x^2-242x-66x=0

We add all the numbers together, and all the variables

1012x^2-308x=0

a = 1012; b = -308; c = 0;
Δ = b2-4ac
Δ = -3082-4·1012·0
Δ = 94864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{94864}=308$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-308)-308}{2*1012}=\frac{0}{2024}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-308)+308}{2*1012}=\frac{616}{2024}
=7/23
$