1/2m+5(m-2)=1

Solution for 1/2m+5(m-2)=1 equation:

1/2m+5(m-2)=1

We move all terms to the left:

1/2m+5(m-2)-(1)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We multiply parentheses

1/2m+5m-10-1=0

We multiply all the terms by the denominator


5m*2m-10*2m-1*2m+1=0

Wy multiply elements

10m^2-20m-2m+1=0

We add all the numbers together, and all the variables

10m^2-22m+1=0

a = 10; b = -22; c = +1;
Δ = b2-4ac
Δ = -222-4·10·1
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{111}}{2*10}=\frac{22-2\sqrt{111}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{111}}{2*10}=\frac{22+2\sqrt{111}}{20}
$