8/m+10=4/2m-7

Solution for 8/m+10=4/2m-7 equation:

8/m+10=4/2m-7

We move all terms to the left:

8/m+10-(4/2m-7)=0


Domain of the equation: m!=0

m∈R



Domain of the equation: 2m-7)!=0

m∈R


We get rid of parentheses

8/m-4/2m+7+10=0

We calculate fractions


16m/2m^2+(-4m)/2m^2+7+10=0

We add all the numbers together, and all the variables

16m/2m^2+(-4m)/2m^2+17=0

We multiply all the terms by the denominator


16m+(-4m)+17*2m^2=0

Wy multiply elements

34m^2+16m+(-4m)=0

We get rid of parentheses

34m^2+16m-4m=0

We add all the numbers together, and all the variables

34m^2+12m=0

a = 34; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·34·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*34}=\frac{-24}{68}
=-6/17
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*34}=\frac{0}{68}
=0
$