8/3m-2/5=1/5m-4

Solution for 8/3m-2/5=1/5m-4 equation:

8/3m-2/5=1/5m-4

We move all terms to the left:

8/3m-2/5-(1/5m-4)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 5m-4)!=0

m∈R


We get rid of parentheses

8/3m-1/5m+4-2/5=0

We calculate fractions


1000m/375m^2+(-3m)/375m^2+(-6m)/375m^2+4=0

We multiply all the terms by the denominator


1000m+(-3m)+(-6m)+4*375m^2=0

Wy multiply elements

1500m^2+1000m+(-3m)+(-6m)=0

We get rid of parentheses

1500m^2+1000m-3m-6m=0

We add all the numbers together, and all the variables

1500m^2+991m=0

a = 1500; b = 991; c = 0;
Δ = b2-4ac
Δ = 9912-4·1500·0
Δ = 982081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{982081}=991$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(991)-991}{2*1500}=\frac{-1982}{3000}
=-991/1500
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(991)+991}{2*1500}=\frac{0}{3000}
=0
$