m+7/m+6=-10/5

Solution for m+7/m+6=-10/5 equation:

m+7/m+6=-10/5

We move all terms to the left:

m+7/m+6-(-10/5)=0


Domain of the equation: m!=0

m∈R


We add all the numbers together, and all the variables

m+7/m+6-(-2)=0

We add all the numbers together, and all the variables

m+7/m+8=0

We multiply all the terms by the denominator


m*m+8*m+7=0

We add all the numbers together, and all the variables

8m+m*m+7=0

Wy multiply elements

m^2+8m+7=0

a = 1; b = 8; c = +7;
Δ = b2-4ac
Δ = 82-4·1·7
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6}{2*1}=\frac{-14}{2}
=-7
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6}{2*1}=\frac{-2}{2}
=-1
$