5/6m-1/2m+1=4

Solution for 5/6m-1/2m+1=4 equation:

5/6m-1/2m+1=4

We move all terms to the left:

5/6m-1/2m+1-(4)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

5/6m-1/2m-3=0

We calculate fractions


10m/12m^2+(-6m)/12m^2-3=0

We multiply all the terms by the denominator


10m+(-6m)-3*12m^2=0

Wy multiply elements

-36m^2+10m+(-6m)=0

We get rid of parentheses

-36m^2+10m-6m=0

We add all the numbers together, and all the variables

-36m^2+4m=0

a = -36; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-36)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-36}=\frac{-8}{-72}
=1/9
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-36}=\frac{0}{-72}
=0
$