6/5m-6=2/3m+10

Solution for 6/5m-6=2/3m+10 equation:

6/5m-6=2/3m+10

We move all terms to the left:

6/5m-6-(2/3m+10)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 3m+10)!=0

m∈R


We get rid of parentheses

6/5m-2/3m-10-6=0

We calculate fractions


18m/15m^2+(-10m)/15m^2-10-6=0

We add all the numbers together, and all the variables

18m/15m^2+(-10m)/15m^2-16=0

We multiply all the terms by the denominator


18m+(-10m)-16*15m^2=0

Wy multiply elements

-240m^2+18m+(-10m)=0

We get rid of parentheses

-240m^2+18m-10m=0

We add all the numbers together, and all the variables

-240m^2+8m=0

a = -240; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-240)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-240}=\frac{-16}{-480}
=1/30
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-240}=\frac{0}{-480}
=0
$