m/2m+0.5(m-4)=9

Solution for m/2m+0.5(m-4)=9 equation:

m/2m+0.5(m-4)=9

We move all terms to the left:

m/2m+0.5(m-4)-(9)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We multiply parentheses

m/2m+0.5m-2-9=0

We multiply all the terms by the denominator


m+(0.5m)*2m-2*2m-9*2m=0

We add all the numbers together, and all the variables

m+(+0.5m)*2m-2*2m-9*2m=0

We multiply parentheses

0m^2+m-2*2m-9*2m=0

Wy multiply elements

0m^2+m-4m-18m=0

We add all the numbers together, and all the variables

m^2-21m=0

a = 1; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·1·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*1}=\frac{0}{2}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*1}=\frac{42}{2}
=21
$