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

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

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

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2m^2*5-4=0

Wy multiply elements

10m^2-4=0

a = 10; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·10·(-4)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*10}=\frac{0-4\sqrt{10}}{20}
=-\frac{4\sqrt{10}}{20}
=-\frac{\sqrt{10}}{5}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*10}=\frac{0+4\sqrt{10}}{20}
=\frac{4\sqrt{10}}{20}
=\frac{\sqrt{10}}{5}
$