4-3/5m=6/6m+2

Solution for 4-3/5m=6/6m+2 equation:

4-3/5m=6/6m+2

We move all terms to the left:

4-3/5m-(6/6m+2)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 6m+2)!=0

m∈R


We get rid of parentheses

-3/5m-6/6m-2+4=0

We calculate fractions


(-18m)/30m^2+(-30m)/30m^2-2+4=0

We add all the numbers together, and all the variables

(-18m)/30m^2+(-30m)/30m^2+2=0

We multiply all the terms by the denominator


(-18m)+(-30m)+2*30m^2=0

Wy multiply elements

60m^2+(-18m)+(-30m)=0

We get rid of parentheses

60m^2-18m-30m=0

We add all the numbers together, and all the variables

60m^2-48m=0

a = 60; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·60·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*60}=\frac{0}{120}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*60}=\frac{96}{120}
=4/5
$