2/3x-17=2x-29x

Solution for 2/3x-17=2x-29x equation:

2/3x-17=2x-29x

We move all terms to the left:

2/3x-17-(2x-29x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-27x)-17=0

We get rid of parentheses

2/3x+27x-17=0

We multiply all the terms by the denominator


27x*3x-17*3x+2=0

Wy multiply elements

81x^2-51x+2=0

a = 81; b = -51; c = +2;
Δ = b2-4ac
Δ = -512-4·81·2
Δ = 1953
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:

$\sqrt{\Delta}=\sqrt{1953}=\sqrt{9*217}=\sqrt{9}*\sqrt{217}=3\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{217}}{2*81}=\frac{51-3\sqrt{217}}{162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{217}}{2*81}=\frac{51+3\sqrt{217}}{162}
$