(5/3x)+x=64

Solution for (5/3x)+x=64 equation:

(5/3x)+x=64

We move all terms to the left:

(5/3x)+x-(64)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/3x)+x-64=0

We add all the numbers together, and all the variables

x+(+5/3x)-64=0

We get rid of parentheses

x+5/3x-64=0

We multiply all the terms by the denominator


x*3x-64*3x+5=0

Wy multiply elements

3x^2-192x+5=0

a = 3; b = -192; c = +5;
Δ = b2-4ac
Δ = -1922-4·3·5
Δ = 36804
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:

$\sqrt{\Delta}=\sqrt{36804}=\sqrt{4*9201}=\sqrt{4}*\sqrt{9201}=2\sqrt{9201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-2\sqrt{9201}}{2*3}=\frac{192-2\sqrt{9201}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+2\sqrt{9201}}{2*3}=\frac{192+2\sqrt{9201}}{6}
$