11+m=1/4m-3m

Solution for 11+m=1/4m-3m equation:

11+m=1/4m-3m

We move all terms to the left:

11+m-(1/4m-3m)=0


Domain of the equation: 4m-3m)!=0

m∈R


We add all the numbers together, and all the variables

m-(-3m+1/4m)+11=0

We get rid of parentheses

m+3m-1/4m+11=0

We multiply all the terms by the denominator


m*4m+3m*4m+11*4m-1=0

Wy multiply elements

4m^2+12m^2+44m-1=0

We add all the numbers together, and all the variables

16m^2+44m-1=0

a = 16; b = 44; c = -1;
Δ = b2-4ac
Δ = 442-4·16·(-1)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-20\sqrt{5}}{2*16}=\frac{-44-20\sqrt{5}}{32}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+20\sqrt{5}}{2*16}=\frac{-44+20\sqrt{5}}{32}
$