6m-7-(3/m)=0

Solution for 6m-7-(3/m)=0 equation:

6m-7-(3/m)=0


Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

6m-(+3/m)-7=0

We get rid of parentheses

6m-3/m-7=0

We multiply all the terms by the denominator


6m*m-7*m-3=0

We add all the numbers together, and all the variables

-7m+6m*m-3=0

Wy multiply elements

6m^2-7m-3=0

a = 6; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·6·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*6}=\frac{-4}{12}
=-1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*6}=\frac{18}{12}
=1+1/2
$