6/12x+4=2/11x+16

Solution for 6/12x+4=2/11x+16 equation:

6/12x+4=2/11x+16

We move all terms to the left:

6/12x+4-(2/11x+16)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 11x+16)!=0

x∈R


We get rid of parentheses

6/12x-2/11x-16+4=0

We calculate fractions


66x/132x^2+(-24x)/132x^2-16+4=0

We add all the numbers together, and all the variables

66x/132x^2+(-24x)/132x^2-12=0

We multiply all the terms by the denominator


66x+(-24x)-12*132x^2=0

Wy multiply elements

-1584x^2+66x+(-24x)=0

We get rid of parentheses

-1584x^2+66x-24x=0

We add all the numbers together, and all the variables

-1584x^2+42x=0

a = -1584; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-1584)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-1584}=\frac{-84}{-3168}
=7/264
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-1584}=\frac{0}{-3168}
=0
$