3m=5/m-10

Solution for 3m=5/m-10 equation:

3m=5/m-10

We move all terms to the left:

3m-(5/m-10)=0


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

m∈R


We get rid of parentheses

3m-5/m+10=0

We multiply all the terms by the denominator


3m*m+10*m-5=0

We add all the numbers together, and all the variables

10m+3m*m-5=0

Wy multiply elements

3m^2+10m-5=0

a = 3; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·3·(-5)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{10}}{2*3}=\frac{-10-4\sqrt{10}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{10}}{2*3}=\frac{-10+4\sqrt{10}}{6}
$