3/10m=16-1/5m

Solution for 3/10m=16-1/5m equation:

3/10m=16-1/5m

We move all terms to the left:

3/10m-(16-1/5m)=0


Domain of the equation: 10m!=0

m!=0/10

m!=0

m∈R



Domain of the equation: 5m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

3/10m-(-1/5m+16)=0

We get rid of parentheses

3/10m+1/5m-16=0

We calculate fractions


15m/50m^2+10m/50m^2-16=0

We multiply all the terms by the denominator


15m+10m-16*50m^2=0

We add all the numbers together, and all the variables

25m-16*50m^2=0

Wy multiply elements

-800m^2+25m=0

a = -800; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-800)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-800}=\frac{-50}{-1600}
=1/32
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-800}=\frac{0}{-1600}
=0
$