5/6m-5/2m=-55/12

Solution for 5/6m-5/2m=-55/12 equation:

5/6m-5/2m=-55/12

We move all terms to the left:

5/6m-5/2m-(-55/12)=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 get rid of parentheses

5/6m-5/2m+55/12=0

We calculate fractions


1320m^2/144m^2+120m/144m^2+(-360m)/144m^2=0

We multiply all the terms by the denominator


1320m^2+120m+(-360m)=0

We get rid of parentheses

1320m^2+120m-360m=0

We add all the numbers together, and all the variables

1320m^2-240m=0

a = 1320; b = -240; c = 0;
Δ = b2-4ac
Δ = -2402-4·1320·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-240}{2*1320}=\frac{0}{2640}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+240}{2*1320}=\frac{480}{2640}
=2/11
$