m+15=3/5m+9

Solution for m+15=3/5m+9 equation:

m+15=3/5m+9

We move all terms to the left:

m+15-(3/5m+9)=0


Domain of the equation: 5m+9)!=0

m∈R


We get rid of parentheses

m-3/5m-9+15=0

We multiply all the terms by the denominator


m*5m-9*5m+15*5m-3=0

Wy multiply elements

5m^2-45m+75m-3=0

We add all the numbers together, and all the variables

5m^2+30m-3=0

a = 5; b = 30; c = -3;
Δ = b2-4ac
Δ = 302-4·5·(-3)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-8\sqrt{15}}{2*5}=\frac{-30-8\sqrt{15}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+8\sqrt{15}}{2*5}=\frac{-30+8\sqrt{15}}{10}
$