2m+(-1/2m-11)=-5

Solution for 2m+(-1/2m-11)=-5 equation:

2m+(-1/2m-11)=-5

We move all terms to the left:

2m+(-1/2m-11)-(-5)=0


Domain of the equation: 2m-11)!=0

m∈R


We add all the numbers together, and all the variables

2m+(-1/2m-11)+5=0

We get rid of parentheses

2m-1/2m-11+5=0

We multiply all the terms by the denominator


2m*2m-11*2m+5*2m-1=0

Wy multiply elements

4m^2-22m+10m-1=0

We add all the numbers together, and all the variables

4m^2-12m-1=0

a = 4; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·4·(-1)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*4}=\frac{12-4\sqrt{10}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*4}=\frac{12+4\sqrt{10}}{8}
$