11/5m-2/3m=16

Solution for 11/5m-2/3m=16 equation:

11/5m-2/3m=16

We move all terms to the left:

11/5m-2/3m-(16)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We calculate fractions


33m/15m^2+(-10m)/15m^2-16=0

We multiply all the terms by the denominator


33m+(-10m)-16*15m^2=0

Wy multiply elements

-240m^2+33m+(-10m)=0

We get rid of parentheses

-240m^2+33m-10m=0

We add all the numbers together, and all the variables

-240m^2+23m=0

a = -240; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-240)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-240}=\frac{-46}{-480}
=23/240
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-240}=\frac{0}{-480}
=0
$