1/3x-6/3+1/2x+5/10=5/3

Solution for 1/3x-6/3+1/2x+5/10=5/3 equation:

1/3x-6/3+1/2x+5/10=5/3

We move all terms to the left:

1/3x-6/3+1/2x+5/10-(5/3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x+1/2x-6/3+5/10-(+5/3)=0

We add all the numbers together, and all the variables

1/3x+1/2x-2+5/10-(+5/3)=0

We get rid of parentheses

1/3x+1/2x-2+5/10-5/3=0

We calculate fractions


180x^2/180x^2+20x/180x^2+90x/180x^2+(-100x)/180x^2-2=0

Fractions to decimals

20x/180x^2+90x/180x^2+(-100x)/180x^2-2+1=0

We multiply all the terms by the denominator


20x+90x+(-100x)-2*180x^2+1*180x^2=0

We add all the numbers together, and all the variables

110x+(-100x)-2*180x^2+1*180x^2=0

Wy multiply elements

-360x^2+180x^2+110x+(-100x)=0

We get rid of parentheses

-360x^2+180x^2+110x-100x=0

We add all the numbers together, and all the variables

-180x^2+10x=0

a = -180; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-180)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-180}=\frac{-20}{-360}
=1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-180}=\frac{0}{-360}
=0
$