(4/5)x+(2/3)=2

Solution for (4/5)x+(2/3)=2 equation:

(4/5)x+(2/3)=2

We move all terms to the left:

(4/5)x+(2/3)-(2)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(4/5)x-2+(2/3)=0

We add all the numbers together, and all the variables

(+4/5)x-2+(+2/3)=0

We multiply parentheses

4x^2-2+(+2/3)=0

We get rid of parentheses

4x^2-2+2/3=0

We multiply all the terms by the denominator


4x^2*3+2-2*3=0

We add all the numbers together, and all the variables

4x^2*3-4=0

Wy multiply elements

12x^2-4=0

a = 12; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·12·(-4)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*12}=\frac{0-8\sqrt{3}}{24}
=-\frac{8\sqrt{3}}{24}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*12}=\frac{0+8\sqrt{3}}{24}
=\frac{8\sqrt{3}}{24}
=\frac{\sqrt{3}}{3}
$