0.5m-2.5=5/4m+2

Solution for 0.5m-2.5=5/4m+2 equation:

0.5m-2.5=5/4m+2

We move all terms to the left:

0.5m-2.5-(5/4m+2)=0


Domain of the equation: 4m+2)!=0

m∈R


We get rid of parentheses

0.5m-5/4m-2-2.5=0

We multiply all the terms by the denominator


(0.5m)*4m-2*4m-(2.5)*4m-5=0

We add all the numbers together, and all the variables

(+0.5m)*4m-2*4m-(2.5)*4m-5=0

We multiply parentheses

0m^2-2*4m-10m-5=0

Wy multiply elements

0m^2-8m-10m-5=0

We add all the numbers together, and all the variables

m^2-18m-5=0

a = 1; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·1·(-5)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{86}}{2*1}=\frac{18-2\sqrt{86}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{86}}{2*1}=\frac{18+2\sqrt{86}}{2}
$