3m+5=8/m

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

3m+5=8/m

We move all terms to the left:

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


Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3m-8/m+5=0

We multiply all the terms by the denominator


3m*m+5*m-8=0

We add all the numbers together, and all the variables

5m+3m*m-8=0

Wy multiply elements

3m^2+5m-8=0

a = 3; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·3·(-8)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*3}=\frac{-16}{6}
=-2+2/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*3}=\frac{6}{6}
=1
$