10/3x+5/24x+5/2=10/3

Solution for 10/3x+5/24x+5/2=10/3 equation:

10/3x+5/24x+5/2=10/3

We move all terms to the left:

10/3x+5/24x+5/2-(10/3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 24x!=0

x!=0/24

x!=0

x∈R


We add all the numbers together, and all the variables

10/3x+5/24x+5/2-(+10/3)=0

We get rid of parentheses

10/3x+5/24x+5/2-10/3=0

We calculate fractions


2160x^2/864x^2+960x/864x^2+180x/864x^2+(-960x)/864x^2=0

We multiply all the terms by the denominator


2160x^2+960x+180x+(-960x)=0

We add all the numbers together, and all the variables

2160x^2+1140x+(-960x)=0

We get rid of parentheses

2160x^2+1140x-960x=0

We add all the numbers together, and all the variables

2160x^2+180x=0

a = 2160; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·2160·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*2160}=\frac{-360}{4320}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*2160}=\frac{0}{4320}
=0
$