(5/6)x-4x+(8/3)=(5/3)

Solution for (5/6)x-4x+(8/3)=(5/3) equation:

(5/6)x-4x+(8/3)=(5/3)

We move all terms to the left:

(5/6)x-4x+(8/3)-((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-4x+(+8/3)-((+5/3))=0

We add all the numbers together, and all the variables

-4x+(+5/6)x+(+8/3)-((+5/3))=0

We multiply parentheses

5x^2-4x+(+8/3)-((+5/3))=0

We get rid of parentheses

5x^2-4x+8/3-((+5/3))=0

We calculate fractions


5x^2-4x=0

a = 5; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·5·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*5}=\frac{8}{10}
=4/5
$