1/3m=5m+13

Solution for 1/3m=5m+13 equation:

1/3m=5m+13

We move all terms to the left:

1/3m-(5m+13)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We get rid of parentheses

1/3m-5m-13=0

We multiply all the terms by the denominator


-5m*3m-13*3m+1=0

Wy multiply elements

-15m^2-39m+1=0

a = -15; b = -39; c = +1;
Δ = b2-4ac
Δ = -392-4·(-15)·1
Δ = 1581
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1581}}{2*-15}=\frac{39-\sqrt{1581}}{-30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1581}}{2*-15}=\frac{39+\sqrt{1581}}{-30}
$