11+m=1/4m-

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

11+m=1/4m-

We move all terms to the left:

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


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

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

m-1/4m+11=0

We multiply all the terms by the denominator


m*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 = 1952
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:

$\sqrt{\Delta}=\sqrt{1952}=\sqrt{16*122}=\sqrt{16}*\sqrt{122}=4\sqrt{122}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{122}}{2*4}=\frac{-44-4\sqrt{122}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{122}}{2*4}=\frac{-44+4\sqrt{122}}{8}
$