1/2m+2=4/5m+5

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

1/2m+2=4/5m+5

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 5m+5)!=0

m∈R


We get rid of parentheses

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

We calculate fractions


5m/10m^2+(-8m)/10m^2-5+2=0

We add all the numbers together, and all the variables

5m/10m^2+(-8m)/10m^2-3=0

We multiply all the terms by the denominator


5m+(-8m)-3*10m^2=0

Wy multiply elements

-30m^2+5m+(-8m)=0

We get rid of parentheses

-30m^2+5m-8m=0

We add all the numbers together, and all the variables

-30m^2-3m=0

a = -30; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-30)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-30}=\frac{0}{-60}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-30}=\frac{6}{-60}
=-1/10
$