(5/3x-6)-(4/2-x)=0

Solution for (5/3x-6)-(4/2-x)=0 equation:

(5/3x-6)-(4/2-x)=0


Domain of the equation: 3x-6)!=0

x∈R



Domain of the equation: 2-x)!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-2

x!=-2/1

x!=-2

x∈R


We add all the numbers together, and all the variables

(5/3x-6)-(-1x+2)=0

We get rid of parentheses

5/3x+1x-6-2=0

We multiply all the terms by the denominator


1x*3x-6*3x-2*3x+5=0

Wy multiply elements

3x^2-18x-6x+5=0

We add all the numbers together, and all the variables

3x^2-24x+5=0

a = 3; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·3·5
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{129}}{2*3}=\frac{24-2\sqrt{129}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{129}}{2*3}=\frac{24+2\sqrt{129}}{6}
$