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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


5x^2*3-4x*3+4-5=0

We add all the numbers together, and all the variables

5x^2*3-4x*3-1=0

Wy multiply elements

15x^2-12x-1=0

a = 15; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·15·(-1)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{51}}{2*15}=\frac{12-2\sqrt{51}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{51}}{2*15}=\frac{12+2\sqrt{51}}{30}
$