11+m=1/4m+2m

Solution for 11+m=1/4m+2m equation:

11+m=1/4m+2m

We move all terms to the left:

11+m-(1/4m+2m)=0


Domain of the equation: 4m+2m)!=0

m∈R


We add all the numbers together, and all the variables

m-(+2m+1/4m)+11=0

We get rid of parentheses

m-2m-1/4m+11=0

We multiply all the terms by the denominator


m*4m-2m*4m+11*4m-1=0

Wy multiply elements

4m^2-8m^2+44m-1=0

We add all the numbers together, and all the variables

-4m^2+44m-1=0

a = -4; b = 44; c = -1;
Δ = b2-4ac
Δ = 442-4·(-4)·(-1)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-8\sqrt{30}}{2*-4}=\frac{-44-8\sqrt{30}}{-8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+8\sqrt{30}}{2*-4}=\frac{-44+8\sqrt{30}}{-8}
$