(1/3)x-(2/3)=10

Solution for (1/3)x-(2/3)=10 equation:

(1/3)x-(2/3)=10

We move all terms to the left:

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


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(1/3)x-10-(2/3)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2-10-(+2/3)=0

We get rid of parentheses

x^2-10-2/3=0

We multiply all the terms by the denominator


x^2*3-2-10*3=0

We add all the numbers together, and all the variables

x^2*3-32=0

Wy multiply elements

3x^2-32=0

a = 3; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·3·(-32)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*3}=\frac{0-8\sqrt{6}}{6}
=-\frac{8\sqrt{6}}{6}
=-\frac{4\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*3}=\frac{0+8\sqrt{6}}{6}
=\frac{8\sqrt{6}}{6}
=\frac{4\sqrt{6}}{3}
$