1/3x+12(2)-2x=-18+3x

Solution for 1/3x+12(2)-2x=-18+3x equation:

1/3x+12(2)-2x=-18+3x

We move all terms to the left:

1/3x+12(2)-2x-(-18+3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-2x-(3x-18)+122=0

We add all the numbers together, and all the variables

-2x+1/3x-(3x-18)+122=0

We get rid of parentheses

-2x+1/3x-3x+18+122=0

We multiply all the terms by the denominator


-2x*3x-3x*3x+18*3x+122*3x+1=0

Wy multiply elements

-6x^2-9x^2+54x+366x+1=0

We add all the numbers together, and all the variables

-15x^2+420x+1=0

a = -15; b = 420; c = +1;
Δ = b2-4ac
Δ = 4202-4·(-15)·1
Δ = 176460
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:

$\sqrt{\Delta}=\sqrt{176460}=\sqrt{4*44115}=\sqrt{4}*\sqrt{44115}=2\sqrt{44115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(420)-2\sqrt{44115}}{2*-15}=\frac{-420-2\sqrt{44115}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(420)+2\sqrt{44115}}{2*-15}=\frac{-420+2\sqrt{44115}}{-30}
$