(1/5)x+4/5=6/5

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Solution for (1/5)x+4/5=6/5 equation: 



(1/5)x+4/5=6/5

We move all terms to the left:

(1/5)x+4/5-(6/5)=0



Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

(+1/5)x+4/5-(+6/5)=0

We multiply parentheses

x^2+4/5-(+6/5)=0

We get rid of parentheses

x^2+4/5-6/5=0

We multiply all the terms by the denominator


x^2*5+4-6=0

We add all the numbers together, and all the variables

x^2*5-2=0

Wy multiply elements

5x^2-2=0

a = 5; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·5·(-2)
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:


$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*5}=\frac{0-2\sqrt{10}}{10}
=-\frac{2\sqrt{10}}{10}
=-\frac{\sqrt{10}}{5}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*5}=\frac{0+2\sqrt{10}}{10}
=\frac{2\sqrt{10}}{10}
=\frac{\sqrt{10}}{5}
$

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