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

We move all terms containing m to the left, all other terms to the right

m!=-9

m∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We multiply parentheses

-m^2-9m-10m-90+7=0

We add all the numbers together, and all the variables

-1m^2-19m-83=0

a = -1; b = -19; c = -83;
Δ = b2-4ac
Δ = -192-4·(-1)·(-83)
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{29}}{2*-1}=\frac{19-\sqrt{29}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{29}}{2*-1}=\frac{19+\sqrt{29}}{-2}
$