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

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

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

We move all terms to the left:

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


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x^2*3-8=0

Wy multiply elements

15x^2-8=0

a = 15; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·15·(-8)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*15}=\frac{0-4\sqrt{30}}{30}
=-\frac{4\sqrt{30}}{30}
=-\frac{2\sqrt{30}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*15}=\frac{0+4\sqrt{30}}{30}
=\frac{4\sqrt{30}}{30}
=\frac{2\sqrt{30}}{15}
$