1/5m=10/60m+1

Solution for 1/5m=10/60m+1 equation:

1/5m=10/60m+1

We move all terms to the left:

1/5m-(10/60m+1)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 60m+1)!=0

m∈R


We get rid of parentheses

1/5m-10/60m-1=0

We calculate fractions


60m/300m^2+(-50m)/300m^2-1=0

We multiply all the terms by the denominator


60m+(-50m)-1*300m^2=0

Wy multiply elements

-300m^2+60m+(-50m)=0

We get rid of parentheses

-300m^2+60m-50m=0

We add all the numbers together, and all the variables

-300m^2+10m=0

a = -300; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-300)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-300}=\frac{-20}{-600}
=1/30
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-300}=\frac{0}{-600}
=0
$