5m-15/m=10

Solution for 5m-15/m=10 equation:

5m-15/m=10

We move all terms to the left:

5m-15/m-(10)=0


Domain of the equation: m!=0

m∈R


We multiply all the terms by the denominator


5m*m-10*m-15=0

We add all the numbers together, and all the variables

-10m+5m*m-15=0

Wy multiply elements

5m^2-10m-15=0

a = 5; b = -10; c = -15;
Δ = b2-4ac
Δ = -102-4·5·(-15)
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{-(-10)-20}{2*5}=\frac{-10}{10}
=-1
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*5}=\frac{30}{10}
=3
$