(1/3x)+x=4.8

Solution for (1/3x)+x=4.8 equation:

(1/3x)+x=4.8

We move all terms to the left:

(1/3x)+x-(4.8)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3x)+x-(4.8)=0

We add all the numbers together, and all the variables

x+(+1/3x)-4.8=0

We get rid of parentheses

x+1/3x-4.8=0

We multiply all the terms by the denominator


x*3x-(4.8)*3x+1=0

We multiply parentheses

x*3x-14.4x+1=0

Wy multiply elements

3x^2-14.4x+1=0

a = 3; b = -14.4; c = +1;
Δ = b2-4ac
Δ = -14.42-4·3·1
Δ = 195.36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14.4)-\sqrt{195.36}}{2*3}=\frac{14.4-\sqrt{195.36}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14.4)+\sqrt{195.36}}{2*3}=\frac{14.4+\sqrt{195.36}}{6}
$