(2/5)x-2=8/3

Solution for (2/5)x-2=8/3 equation:

(2/5)x-2=8/3

We move all terms to the left:

(2/5)x-2-(8/3)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

2x^2-2-8/3=0

We multiply all the terms by the denominator


2x^2*3-8-2*3=0

We add all the numbers together, and all the variables

2x^2*3-14=0

Wy multiply elements

6x^2-14=0

a = 6; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·6·(-14)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*6}=\frac{0-4\sqrt{21}}{12}
=-\frac{4\sqrt{21}}{12}
=-\frac{\sqrt{21}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*6}=\frac{0+4\sqrt{21}}{12}
=\frac{4\sqrt{21}}{12}
=\frac{\sqrt{21}}{3}
$