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

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

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

We move all terms to the left:

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


Domain of the equation: 11m!=0

m!=0/11

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

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

16m*11m-4*11m-4=0

Wy multiply elements

176m^2-44m-4=0

a = 176; b = -44; c = -4;
Δ = b2-4ac
Δ = -442-4·176·(-4)
Δ = 4752
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4752}=\sqrt{144*33}=\sqrt{144}*\sqrt{33}=12\sqrt{33}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-12\sqrt{33}}{2*176}=\frac{44-12\sqrt{33}}{352}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+12\sqrt{33}}{2*176}=\frac{44+12\sqrt{33}}{352}
$