1/6m-5+2/3m=10

Solution for 1/6m-5+2/3m=10 equation:

1/6m-5+2/3m=10

We move all terms to the left:

1/6m-5+2/3m-(10)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

1/6m+2/3m-15=0

We calculate fractions


3m/18m^2+12m/18m^2-15=0

We multiply all the terms by the denominator


3m+12m-15*18m^2=0

We add all the numbers together, and all the variables

15m-15*18m^2=0

Wy multiply elements

-270m^2+15m=0

a = -270; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-270)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-270}=\frac{-30}{-540}
=1/18
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-270}=\frac{0}{-540}
=0
$