5/3x+x=32

Solution for 5/3x+x=32 equation:

5/3x+x=32

We move all terms to the left:

5/3x+x-(32)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+5/3x-32=0

We multiply all the terms by the denominator


x*3x-32*3x+5=0

Wy multiply elements

3x^2-96x+5=0

a = 3; b = -96; c = +5;
Δ = b2-4ac
Δ = -962-4·3·5
Δ = 9156
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:

$\sqrt{\Delta}=\sqrt{9156}=\sqrt{4*2289}=\sqrt{4}*\sqrt{2289}=2\sqrt{2289}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2289}}{2*3}=\frac{96-2\sqrt{2289}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2289}}{2*3}=\frac{96+2\sqrt{2289}}{6}
$