m+10=7/m+9

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

m+10=7/m+9

We move all terms to the left:

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


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

m∈R


We get rid of parentheses

m-7/m-9+10=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

m+m*m-7=0

Wy multiply elements

m^2+m-7=0

a = 1; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·1·(-7)
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{-(1)-\sqrt{29}}{2*1}=\frac{-1-\sqrt{29}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{29}}{2*1}=\frac{-1+\sqrt{29}}{2}
$