96=5/3x+x

Solution for 96=5/3x+x equation:

96=5/3x+x

We move all terms to the left:

96-(5/3x+x)=0


Domain of the equation: 3x+x)!=0

x∈R


We add all the numbers together, and all the variables

-(+x+5/3x)+96=0

We get rid of parentheses

-x-5/3x+96=0

We multiply all the terms by the denominator


-x*3x+96*3x-5=0

Wy multiply elements

-3x^2+288x-5=0

a = -3; b = 288; c = -5;
Δ = b2-4ac
Δ = 2882-4·(-3)·(-5)
Δ = 82884
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:

$\sqrt{\Delta}=\sqrt{82884}=\sqrt{4*20721}=\sqrt{4}*\sqrt{20721}=2\sqrt{20721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-2\sqrt{20721}}{2*-3}=\frac{-288-2\sqrt{20721}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+2\sqrt{20721}}{2*-3}=\frac{-288+2\sqrt{20721}}{-6}
$