2/3m+1=-4/5m-10

Solution for 2/3m+1=-4/5m-10 equation:

2/3m+1=-4/5m-10

We move all terms to the left:

2/3m+1-(-4/5m-10)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 5m-10)!=0

m∈R


We get rid of parentheses

2/3m+4/5m+10+1=0

We calculate fractions


10m/15m^2+12m/15m^2+10+1=0

We add all the numbers together, and all the variables

10m/15m^2+12m/15m^2+11=0

We multiply all the terms by the denominator


10m+12m+11*15m^2=0

We add all the numbers together, and all the variables

22m+11*15m^2=0

Wy multiply elements

165m^2+22m=0

a = 165; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·165·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*165}=\frac{-44}{330}
=-2/15
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*165}=\frac{0}{330}
=0
$