10/m-3=6/8m

Solution for 10/m-3=6/8m equation:

10/m-3=6/8m

We move all terms to the left:

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


Domain of the equation: m!=0

m∈R



Domain of the equation: 8m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


80m/8m^2+(-6m)/8m^2-3=0

We multiply all the terms by the denominator


80m+(-6m)-3*8m^2=0

Wy multiply elements

-24m^2+80m+(-6m)=0

We get rid of parentheses

-24m^2+80m-6m=0

We add all the numbers together, and all the variables

-24m^2+74m=0

a = -24; b = 74; c = 0;
Δ = b2-4ac
Δ = 742-4·(-24)·0
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-74}{2*-24}=\frac{-148}{-48}
=3+1/12
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+74}{2*-24}=\frac{0}{-48}
=0
$