4/5m-3=3/10m+7

Solution for 4/5m-3=3/10m+7 equation:

4/5m-3=3/10m+7

We move all terms to the left:

4/5m-3-(3/10m+7)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 10m+7)!=0

m∈R


We get rid of parentheses

4/5m-3/10m-7-3=0

We calculate fractions


40m/50m^2+(-15m)/50m^2-7-3=0

We add all the numbers together, and all the variables

40m/50m^2+(-15m)/50m^2-10=0

We multiply all the terms by the denominator


40m+(-15m)-10*50m^2=0

Wy multiply elements

-500m^2+40m+(-15m)=0

We get rid of parentheses

-500m^2+40m-15m=0

We add all the numbers together, and all the variables

-500m^2+25m=0

a = -500; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-500)·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*-500}=\frac{-50}{-1000}
=1/20
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-500}=\frac{0}{-1000}
=0
$