-2/3m-4=10+1/2m

Solution for -2/3m-4=10+1/2m equation:

-2/3m-4=10+1/2m

We move all terms to the left:

-2/3m-4-(10+1/2m)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

-2/3m-(1/2m+10)-4=0

We get rid of parentheses

-2/3m-1/2m-10-4=0

We calculate fractions


(-4m)/6m^2+(-3m)/6m^2-10-4=0

We add all the numbers together, and all the variables

(-4m)/6m^2+(-3m)/6m^2-14=0

We multiply all the terms by the denominator


(-4m)+(-3m)-14*6m^2=0

Wy multiply elements

-84m^2+(-4m)+(-3m)=0

We get rid of parentheses

-84m^2-4m-3m=0

We add all the numbers together, and all the variables

-84m^2-7m=0

a = -84; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-84)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-84}=\frac{0}{-168}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-84}=\frac{14}{-168}
=-1/12
$