1/3m+3-5m=-15

Solution for 1/3m+3-5m=-15 equation:

1/3m+3-5m=-15

We move all terms to the left:

1/3m+3-5m-(-15)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

-5m+1/3m+18=0

We multiply all the terms by the denominator


-5m*3m+18*3m+1=0

Wy multiply elements

-15m^2+54m+1=0

a = -15; b = 54; c = +1;
Δ = b2-4ac
Δ = 542-4·(-15)·1
Δ = 2976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-4\sqrt{186}}{2*-15}=\frac{-54-4\sqrt{186}}{-30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+4\sqrt{186}}{2*-15}=\frac{-54+4\sqrt{186}}{-30}
$