(10/m+5)+15=3m

Solution for (10/m+5)+15=3m equation:

(10/m+5)+15=3m

We move all terms to the left:

(10/m+5)+15-(3m)=0


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

m∈R


We add all the numbers together, and all the variables

-3m+(10/m+5)+15=0

We get rid of parentheses

-3m+10/m+5+15=0

We multiply all the terms by the denominator


-3m*m+5*m+15*m+10=0

We add all the numbers together, and all the variables

20m-3m*m+10=0

Wy multiply elements

-3m^2+20m+10=0

a = -3; b = 20; c = +10;
Δ = b2-4ac
Δ = 202-4·(-3)·10
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{130}}{2*-3}=\frac{-20-2\sqrt{130}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{130}}{2*-3}=\frac{-20+2\sqrt{130}}{-6}
$