3/10m-12=4/5m-5

Solution for 3/10m-12=4/5m-5 equation:

3/10m-12=4/5m-5

We move all terms to the left:

3/10m-12-(4/5m-5)=0


Domain of the equation: 10m!=0

m!=0/10

m!=0

m∈R



Domain of the equation: 5m-5)!=0

m∈R


We get rid of parentheses

3/10m-4/5m+5-12=0

We calculate fractions


15m/50m^2+(-40m)/50m^2+5-12=0

We add all the numbers together, and all the variables

15m/50m^2+(-40m)/50m^2-7=0

We multiply all the terms by the denominator


15m+(-40m)-7*50m^2=0

Wy multiply elements

-350m^2+15m+(-40m)=0

We get rid of parentheses

-350m^2+15m-40m=0

We add all the numbers together, and all the variables

-350m^2-25m=0

a = -350; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-350)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-350}=\frac{0}{-700}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-350}=\frac{50}{-700}
=-1/14
$