1/6m-4+3m=16

Solution for 1/6m-4+3m=16 equation:

1/6m-4+3m=16

We move all terms to the left:

1/6m-4+3m-(16)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R


We add all the numbers together, and all the variables

3m+1/6m-20=0

We multiply all the terms by the denominator


3m*6m-20*6m+1=0

Wy multiply elements

18m^2-120m+1=0

a = 18; b = -120; c = +1;
Δ = b2-4ac
Δ = -1202-4·18·1
Δ = 14328
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:

$\sqrt{\Delta}=\sqrt{14328}=\sqrt{36*398}=\sqrt{36}*\sqrt{398}=6\sqrt{398}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-6\sqrt{398}}{2*18}=\frac{120-6\sqrt{398}}{36}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+6\sqrt{398}}{2*18}=\frac{120+6\sqrt{398}}{36}
$