(1/3)x+(1/5)=1

Solution for (1/3)x+(1/5)=1 equation:

(1/3)x+(1/5)=1

We move all terms to the left:

(1/3)x+(1/5)-(1)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(1/3)x-1+(1/5)=0

We add all the numbers together, and all the variables

(+1/3)x-1+(+1/5)=0

We multiply parentheses

x^2-1+(+1/5)=0

We get rid of parentheses

x^2-1+1/5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x^2*5-4=0

Wy multiply elements

5x^2-4=0

a = 5; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·5·(-4)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*5}=\frac{0-4\sqrt{5}}{10}
=-\frac{4\sqrt{5}}{10}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*5}=\frac{0+4\sqrt{5}}{10}
=\frac{4\sqrt{5}}{10}
=\frac{2\sqrt{5}}{5}
$