8/m+9=10/4m-7

Solution for 8/m+9=10/4m-7 equation:

8/m+9=10/4m-7

We move all terms to the left:

8/m+9-(10/4m-7)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 4m-7)!=0

m∈R


We get rid of parentheses

8/m-10/4m+7+9=0

We calculate fractions


32m/4m^2+(-10m)/4m^2+7+9=0

We add all the numbers together, and all the variables

32m/4m^2+(-10m)/4m^2+16=0

We multiply all the terms by the denominator


32m+(-10m)+16*4m^2=0

Wy multiply elements

64m^2+32m+(-10m)=0

We get rid of parentheses

64m^2+32m-10m=0

We add all the numbers together, and all the variables

64m^2+22m=0

a = 64; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·64·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*64}=\frac{-44}{128}
=-11/32
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*64}=\frac{0}{128}
=0
$