6+4/5m=9/10m

Solution for 6+4/5m=9/10m equation:

6+4/5m=9/10m

We move all terms to the left:

6+4/5m-(9/10m)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 10m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

4/5m-(+9/10m)+6=0

We get rid of parentheses

4/5m-9/10m+6=0

We calculate fractions


40m/50m^2+(-45m)/50m^2+6=0

We multiply all the terms by the denominator


40m+(-45m)+6*50m^2=0

Wy multiply elements

300m^2+40m+(-45m)=0

We get rid of parentheses

300m^2+40m-45m=0

We add all the numbers together, and all the variables

300m^2-5m=0

a = 300; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·300·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*300}=\frac{0}{600}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*300}=\frac{10}{600}
=1/60
$