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

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

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

We move all terms to the left:

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


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

m∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

12m-(-2m+1/4m)=0

We get rid of parentheses

12m+2m-1/4m=0

We multiply all the terms by the denominator


12m*4m+2m*4m-1=0

Wy multiply elements

48m^2+8m^2-1=0

We add all the numbers together, and all the variables

56m^2-1=0

a = 56; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·56·(-1)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*56}=\frac{0-4\sqrt{14}}{112}
=-\frac{4\sqrt{14}}{112}
=-\frac{\sqrt{14}}{28}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*56}=\frac{0+4\sqrt{14}}{112}
=\frac{4\sqrt{14}}{112}
=\frac{\sqrt{14}}{28}
$