6/11x+4=3/22x+6

Solution for 6/11x+4=3/22x+6 equation:

6/11x+4=3/22x+6

We move all terms to the left:

6/11x+4-(3/22x+6)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R



Domain of the equation: 22x+6)!=0

x∈R


We get rid of parentheses

6/11x-3/22x-6+4=0

We calculate fractions


132x/242x^2+(-33x)/242x^2-6+4=0

We add all the numbers together, and all the variables

132x/242x^2+(-33x)/242x^2-2=0

We multiply all the terms by the denominator


132x+(-33x)-2*242x^2=0

Wy multiply elements

-484x^2+132x+(-33x)=0

We get rid of parentheses

-484x^2+132x-33x=0

We add all the numbers together, and all the variables

-484x^2+99x=0

a = -484; b = 99; c = 0;
Δ = b2-4ac
Δ = 992-4·(-484)·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(99)-99}{2*-484}=\frac{-198}{-968}
=9/44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(99)+99}{2*-484}=\frac{0}{-968}
=0
$