11+1/4m=m-2m

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

11+1/4m=m-2m

We move all terms to the left:

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


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/4m+1m+11=0

We multiply all the terms by the denominator


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

Wy multiply elements

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}
$