3/m+10=4/8m+5

Solution for 3/m+10=4/8m+5 equation:

3/m+10=4/8m+5

We move all terms to the left:

3/m+10-(4/8m+5)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 8m+5)!=0

m∈R


We get rid of parentheses

3/m-4/8m-5+10=0

We calculate fractions


24m/8m^2+(-4m)/8m^2-5+10=0

We add all the numbers together, and all the variables

24m/8m^2+(-4m)/8m^2+5=0

We multiply all the terms by the denominator


24m+(-4m)+5*8m^2=0

Wy multiply elements

40m^2+24m+(-4m)=0

We get rid of parentheses

40m^2+24m-4m=0

We add all the numbers together, and all the variables

40m^2+20m=0

a = 40; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·40·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*40}=\frac{-40}{80}
=-1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*40}=\frac{0}{80}
=0
$