(1)/(5m)=(1)/(60m)+1

Solution for (1)/(5m)=(1)/(60m)+1 equation:

(1)/(5m)=(1)/(60m)+1

We move all terms to the left:

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

We calculate fractions


60m/300m^2+(-5m)/300m^2-1=0

We multiply all the terms by the denominator


60m+(-5m)-1*300m^2=0

Wy multiply elements

-300m^2+60m+(-5m)=0

We get rid of parentheses

-300m^2+60m-5m=0

We add all the numbers together, and all the variables

-300m^2+55m=0

a = -300; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·(-300)·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*-300}=\frac{-110}{-600}
=11/60
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*-300}=\frac{0}{-600}
=0
$