1/2m=m+10

Solution for 1/2m=m+10 equation:

1/2m=m+10

We move all terms to the left:

1/2m-(m+10)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We get rid of parentheses

1/2m-m-10=0

We multiply all the terms by the denominator


-m*2m-10*2m+1=0

Wy multiply elements

-2m^2-20m+1=0

a = -2; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-2)·1
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{102}}{2*-2}=\frac{20-2\sqrt{102}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{102}}{2*-2}=\frac{20+2\sqrt{102}}{-4}
$