1/3x+2(3x-2)=15

Solution for 1/3x+2(3x-2)=15 equation:

1/3x+2(3x-2)=15

We move all terms to the left:

1/3x+2(3x-2)-(15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply parentheses

1/3x+6x-4-15=0

We multiply all the terms by the denominator


6x*3x-4*3x-15*3x+1=0

Wy multiply elements

18x^2-12x-45x+1=0

We add all the numbers together, and all the variables

18x^2-57x+1=0

a = 18; b = -57; c = +1;
Δ = b2-4ac
Δ = -572-4·18·1
Δ = 3177
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:

$\sqrt{\Delta}=\sqrt{3177}=\sqrt{9*353}=\sqrt{9}*\sqrt{353}=3\sqrt{353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-3\sqrt{353}}{2*18}=\frac{57-3\sqrt{353}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+3\sqrt{353}}{2*18}=\frac{57+3\sqrt{353}}{36}
$