11=1/4m-2m

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

11=1/4m-2m

We move all terms to the left:

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


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

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2m-1/4m+11=0

We multiply all the terms by the denominator


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

Wy multiply elements

8m^2+44m-1=0

a = 8; b = 44; c = -1;
Δ = b2-4ac
Δ = 442-4·8·(-1)
Δ = 1968
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:

$\sqrt{\Delta}=\sqrt{1968}=\sqrt{16*123}=\sqrt{16}*\sqrt{123}=4\sqrt{123}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{123}}{2*8}=\frac{-44-4\sqrt{123}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{123}}{2*8}=\frac{-44+4\sqrt{123}}{16}
$