(5/6)x-3x+(4/3)=(5/3)

Solution for (5/6)x-3x+(4/3)=(5/3) equation:

(5/6)x-3x+(4/3)=(5/3)

We move all terms to the left:

(5/6)x-3x+(4/3)-((5/3))=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/6)x-3x+(+4/3)-((+5/3))=0

We add all the numbers together, and all the variables

-3x+(+5/6)x+(+4/3)-((+5/3))=0

We multiply parentheses

5x^2-3x+(+4/3)-((+5/3))=0

We get rid of parentheses

5x^2-3x+4/3-((+5/3))=0

We calculate fractions


5x^2-3x=0

a = 5; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·5·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*5}=\frac{6}{10}
=3/5
$