10/3x+x=24

Solution for 10/3x+x=24 equation:

10/3x+x=24

We move all terms to the left:

10/3x+x-(24)=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+10/3x-24=0

We multiply all the terms by the denominator


x*3x-24*3x+10=0

Wy multiply elements

3x^2-72x+10=0

a = 3; b = -72; c = +10;
Δ = b2-4ac
Δ = -722-4·3·10
Δ = 5064
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:

$\sqrt{\Delta}=\sqrt{5064}=\sqrt{4*1266}=\sqrt{4}*\sqrt{1266}=2\sqrt{1266}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1266}}{2*3}=\frac{72-2\sqrt{1266}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1266}}{2*3}=\frac{72+2\sqrt{1266}}{6}
$