11/2m+16=4+6/11m

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

11/2m+16=4+6/11m

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 11m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

11/2m-6/11m-4+16=0

We calculate fractions


121m/22m^2+(-12m)/22m^2-4+16=0

We add all the numbers together, and all the variables

121m/22m^2+(-12m)/22m^2+12=0

We multiply all the terms by the denominator


121m+(-12m)+12*22m^2=0

Wy multiply elements

264m^2+121m+(-12m)=0

We get rid of parentheses

264m^2+121m-12m=0

We add all the numbers together, and all the variables

264m^2+109m=0

a = 264; b = 109; c = 0;
Δ = b2-4ac
Δ = 1092-4·264·0
Δ = 11881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11881}=109$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(109)-109}{2*264}=\frac{-218}{528}
=-109/264
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(109)+109}{2*264}=\frac{0}{528}
=0
$