-2/m+9=7m-8

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

-2/m+9=7m-8

We move all terms to the left:

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


Domain of the equation: m!=0

m∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

17m-7m*m-2=0

Wy multiply elements

-7m^2+17m-2=0

a = -7; b = 17; c = -2;
Δ = b2-4ac
Δ = 172-4·(-7)·(-2)
Δ = 233
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{-(17)-\sqrt{233}}{2*-7}=\frac{-17-\sqrt{233}}{-14}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{233}}{2*-7}=\frac{-17+\sqrt{233}}{-14}
$