7/m=m+10

Solution for 7/m=m+10 equation:

7/m=m+10

We move all terms to the left:

7/m-(m+10)=0


Domain of the equation: m!=0

m∈R


We get rid of parentheses

7/m-m-10=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-10m-m*m+7=0

Wy multiply elements

-1m^2-10m+7=0

a = -1; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·(-1)·7
Δ = 128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8\sqrt{2}}{2*-1}=\frac{10-8\sqrt{2}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8\sqrt{2}}{2*-1}=\frac{10+8\sqrt{2}}{-2}
$