10/m=2m+7

Solution for 10/m=2m+7 equation:

10/m=2m+7

We move all terms to the left:

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


Domain of the equation: m!=0

m∈R


We get rid of parentheses

10/m-2m-7=0

We multiply all the terms by the denominator


-2m*m-7*m+10=0

We add all the numbers together, and all the variables

-7m-2m*m+10=0

Wy multiply elements

-2m^2-7m+10=0

a = -2; b = -7; c = +10;
Δ = b2-4ac
Δ = -72-4·(-2)·10
Δ = 129
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{-(-7)-\sqrt{129}}{2*-2}=\frac{7-\sqrt{129}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{129}}{2*-2}=\frac{7+\sqrt{129}}{-4}
$