5m+1/3m=7

Solution for 5m+1/3m=7 equation:

5m+1/3m=7

We move all terms to the left:

5m+1/3m-(7)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We multiply all the terms by the denominator


5m*3m-7*3m+1=0

Wy multiply elements

15m^2-21m+1=0

a = 15; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·15·1
Δ = 381
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{-(-21)-\sqrt{381}}{2*15}=\frac{21-\sqrt{381}}{30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{381}}{2*15}=\frac{21+\sqrt{381}}{30}
$