(7/(m+9))=m+10

Solution for (7/(m+9))=m+10 equation:

(7/(m+9))=m+10

We move all terms to the left:

(7/(m+9))-(m+10)=0


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

m∈R


We get rid of parentheses

(7/(m+9))-m-10=0

We multiply all the terms by the denominator


(7-m*(m+9))-10*(m+9))=0


We calculate terms in parentheses: +(7-m*(m+9)), so:

7-m*(m+9)

determiningTheFunctionDomain
-m*(m+9)+7

We multiply parentheses

-m^2-9m+7

We add all the numbers together, and all the variables

-1m^2-9m+7

Back to the equation:

+(-1m^2-9m+7)


We multiply parentheses

(-1m^2-9m+7)-10m-=0

We get rid of parentheses

-1m^2-9m-10m+7-=0

We add all the numbers together, and all the variables

-1m^2-19m=0

a = -1; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-1)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-1}=\frac{0}{-2}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-1}=\frac{38}{-2}
=-19
$