2/8m+6=2/3m+10

Solution for 2/8m+6=2/3m+10 equation:

2/8m+6=2/3m+10

We move all terms to the left:

2/8m+6-(2/3m+10)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



Domain of the equation: 3m+10)!=0

m∈R


We get rid of parentheses

2/8m-2/3m-10+6=0

We calculate fractions


6m/24m^2+(-16m)/24m^2-10+6=0

We add all the numbers together, and all the variables

6m/24m^2+(-16m)/24m^2-4=0

We multiply all the terms by the denominator


6m+(-16m)-4*24m^2=0

Wy multiply elements

-96m^2+6m+(-16m)=0

We get rid of parentheses

-96m^2+6m-16m=0

We add all the numbers together, and all the variables

-96m^2-10m=0

a = -96; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-96)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-96}=\frac{0}{-192}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-96}=\frac{20}{-192}
=-5/48
$