11+m=7/4m

Solution for 11+m=7/4m equation:

11+m=7/4m

We move all terms to the left:

11+m-(7/4m)=0


Domain of the equation: 4m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

m-(+7/4m)+11=0

We get rid of parentheses

m-7/4m+11=0

We multiply all the terms by the denominator


m*4m+11*4m-7=0

Wy multiply elements

4m^2+44m-7=0

a = 4; b = 44; c = -7;
Δ = b2-4ac
Δ = 442-4·4·(-7)
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-32\sqrt{2}}{2*4}=\frac{-44-32\sqrt{2}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+32\sqrt{2}}{2*4}=\frac{-44+32\sqrt{2}}{8}
$