(5/6)(x)-(2/3)=1

Solution for (5/6)(x)-(2/3)=1 equation:

(5/6)(x)-(2/3)=1

We move all terms to the left:

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


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

5x^2-1-2/3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x^2*3-5=0

Wy multiply elements

15x^2-5=0

a = 15; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·15·(-5)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*15}=\frac{0-10\sqrt{3}}{30}
=-\frac{10\sqrt{3}}{30}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*15}=\frac{0+10\sqrt{3}}{30}
=\frac{10\sqrt{3}}{30}
=\frac{\sqrt{3}}{3}
$