5+10m=8+20/2m

Solution for 5+10m=8+20/2m equation:

5+10m=8+20/2m

We move all terms to the left:

5+10m-(8+20/2m)=0


Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

10m-(20/2m+8)+5=0

We get rid of parentheses

10m-20/2m-8+5=0

We multiply all the terms by the denominator


10m*2m-8*2m+5*2m-20=0

Wy multiply elements

20m^2-16m+10m-20=0

We add all the numbers together, and all the variables

20m^2-6m-20=0

a = 20; b = -6; c = -20;
Δ = b2-4ac
Δ = -62-4·20·(-20)
Δ = 1636
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:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{409}}{2*20}=\frac{6-2\sqrt{409}}{40}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{409}}{2*20}=\frac{6+2\sqrt{409}}{40}
$