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

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

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

We move all terms to the left:

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


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x^2*3-7=0

Wy multiply elements

6x^2-7=0

a = 6; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·6·(-7)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*6}=\frac{0-2\sqrt{42}}{12}
=-\frac{2\sqrt{42}}{12}
=-\frac{\sqrt{42}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*6}=\frac{0+2\sqrt{42}}{12}
=\frac{2\sqrt{42}}{12}
=\frac{\sqrt{42}}{6}
$