(1/5)x+1/3=4/3

Solution for (1/5)x+1/3=4/3 equation:

(1/5)x+1/3=4/3

We move all terms to the left:

(1/5)x+1/3-(4/3)=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+1/3-(+4/3)=0

We multiply parentheses

x^2+1/3-(+4/3)=0

We get rid of parentheses

x^2+1/3-4/3=0

We multiply all the terms by the denominator


x^2*3+1-4=0

We add all the numbers together, and all the variables

x^2*3-3=0

Wy multiply elements

3x^2-3=0

a = 3; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·3·(-3)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*3}=\frac{6}{6}
=1
$