16(4-3m)=96(-2/3m)

Solution for 16(4-3m)=96(-2/3m) equation:

16(4-3m)=96(-2/3m)

We move all terms to the left:

16(4-3m)-(96(-2/3m))=0


Domain of the equation: 3m))!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

16(-3m+4)-(96(-2/3m))=0

We multiply parentheses

-48m-(96(-2/3m))+64=0

We multiply all the terms by the denominator


-48m*3m))-(96(+64*3m))-2=0

Wy multiply elements

-144m^2+192m=0

a = -144; b = 192; c = 0;
Δ = b2-4ac
Δ = 1922-4·(-144)·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-192}{2*-144}=\frac{-384}{-288}
=1+1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+192}{2*-144}=\frac{0}{-288}
=0
$