-2/m+9=9/7m-8

Solution for -2/m+9=9/7m-8 equation:

-2/m+9=9/7m-8

We move all terms to the left:

-2/m+9-(9/7m-8)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 7m-8)!=0

m∈R


We get rid of parentheses

-2/m-9/7m+8+9=0

We calculate fractions


(-14m)/7m^2+(-9m)/7m^2+8+9=0

We add all the numbers together, and all the variables

(-14m)/7m^2+(-9m)/7m^2+17=0

We multiply all the terms by the denominator


(-14m)+(-9m)+17*7m^2=0

Wy multiply elements

119m^2+(-14m)+(-9m)=0

We get rid of parentheses

119m^2-14m-9m=0

We add all the numbers together, and all the variables

119m^2-23m=0

a = 119; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·119·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*119}=\frac{0}{238}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*119}=\frac{46}{238}
=23/119
$