m-2/5*m=4.5

Solution for m-2/5*m=4.5 equation:

m-2/5m=4.5

We move all terms to the left:

m-2/5m-(4.5)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We add all the numbers together, and all the variables

m-2/5m-4.5=0

We multiply all the terms by the denominator


m*5m-(4.5)*5m-2=0

We multiply parentheses

m*5m-22.5m-2=0

Wy multiply elements

5m^2-22.5m-2=0

a = 5; b = -22.5; c = -2;
Δ = b2-4ac
Δ = -22.52-4·5·(-2)
Δ = 546.25
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{-(-22.5)-\sqrt{546.25}}{2*5}=\frac{22.5-\sqrt{546.25}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22.5)+\sqrt{546.25}}{2*5}=\frac{22.5+\sqrt{546.25}}{10}
$