1/3m-4=3m+16

Solution for 1/3m-4=3m+16 equation:

1/3m-4=3m+16

We move all terms to the left:

1/3m-4-(3m+16)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We get rid of parentheses

1/3m-3m-16-4=0

We multiply all the terms by the denominator


-3m*3m-16*3m-4*3m+1=0

Wy multiply elements

-9m^2-48m-12m+1=0

We add all the numbers together, and all the variables

-9m^2-60m+1=0

a = -9; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·(-9)·1
Δ = 3636
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:

$\sqrt{\Delta}=\sqrt{3636}=\sqrt{36*101}=\sqrt{36}*\sqrt{101}=6\sqrt{101}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6\sqrt{101}}{2*-9}=\frac{60-6\sqrt{101}}{-18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6\sqrt{101}}{2*-9}=\frac{60+6\sqrt{101}}{-18}
$