1/2m-2.5=1.25m+2

Solution for 1/2m-2.5=1.25m+2 equation:

1/2m-2.5=1.25m+2

We move all terms to the left:

1/2m-2.5-(1.25m+2)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We get rid of parentheses

1/2m-1.25m-2-2.5=0

We multiply all the terms by the denominator


-(1.25m)*2m-2*2m-(2.5)*2m+1=0

We add all the numbers together, and all the variables

-(+1.25m)*2m-2*2m-(2.5)*2m+1=0

We multiply parentheses

-2m^2-2*2m-5m+1=0

Wy multiply elements

-2m^2-4m-5m+1=0

We add all the numbers together, and all the variables

-2m^2-9m+1=0

a = -2; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-2)·1
Δ = 89
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{-(-9)-\sqrt{89}}{2*-2}=\frac{9-\sqrt{89}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{89}}{2*-2}=\frac{9+\sqrt{89}}{-4}
$