11+m=1/4m-2

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

11+m=1/4m-2

We move all terms to the left:

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


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

m∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

4m^2+52m-1=0

a = 4; b = 52; c = -1;
Δ = b2-4ac
Δ = 522-4·4·(-1)
Δ = 2720
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:

$\sqrt{\Delta}=\sqrt{2720}=\sqrt{16*170}=\sqrt{16}*\sqrt{170}=4\sqrt{170}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{170}}{2*4}=\frac{-52-4\sqrt{170}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{170}}{2*4}=\frac{-52+4\sqrt{170}}{8}
$