2*(1/3x-2)=-4/3x+2*17

Solution for 2*(1/3x-2)=-4/3x+2*17 equation:

2(1/3x-2)=-4/3x+2*17

We move all terms to the left:

2(1/3x-2)-(-4/3x+2*17)=0


Domain of the equation: 3x-2)!=0

x∈R



Domain of the equation: 3x+2*17)!=0

x∈R


We add all the numbers together, and all the variables

2(1/3x-2)-(-4/3x+34)=0

We multiply parentheses

2x-(-4/3x+34)-4=0

We get rid of parentheses

2x+4/3x-34-4=0

We multiply all the terms by the denominator


2x*3x-34*3x-4*3x+4=0

Wy multiply elements

6x^2-102x-12x+4=0

We add all the numbers together, and all the variables

6x^2-114x+4=0

a = 6; b = -114; c = +4;
Δ = b2-4ac
Δ = -1142-4·6·4
Δ = 12900
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:

$\sqrt{\Delta}=\sqrt{12900}=\sqrt{100*129}=\sqrt{100}*\sqrt{129}=10\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-10\sqrt{129}}{2*6}=\frac{114-10\sqrt{129}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+10\sqrt{129}}{2*6}=\frac{114+10\sqrt{129}}{12}
$