1/8m+2/5+1/2m=3/8m

Solution for 1/8m+2/5+1/2m=3/8m equation:

1/8m+2/5+1/2m=3/8m

We move all terms to the left:

1/8m+2/5+1/2m-(3/8m)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 8m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

1/8m+1/2m-(+3/8m)+2/5=0

We get rid of parentheses

1/8m+1/2m-3/8m+2/5=0

We calculate fractions


64m^2/400m^2+(-150m+1)/400m^2+200m/400m^2=0

We multiply all the terms by the denominator


64m^2+(-150m+1)+200m=0

We add all the numbers together, and all the variables

64m^2+200m+(-150m+1)=0

We get rid of parentheses

64m^2+200m-150m+1=0

We add all the numbers together, and all the variables

64m^2+50m+1=0

a = 64; b = 50; c = +1;
Δ = b2-4ac
Δ = 502-4·64·1
Δ = 2244
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:

$\sqrt{\Delta}=\sqrt{2244}=\sqrt{4*561}=\sqrt{4}*\sqrt{561}=2\sqrt{561}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{561}}{2*64}=\frac{-50-2\sqrt{561}}{128}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{561}}{2*64}=\frac{-50+2\sqrt{561}}{128}
$