12-2/3x=1x-18

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

12-2/3x=1x-18

We move all terms to the left:

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

We get rid of parentheses

-2/3x-x+18+12=0

We multiply all the terms by the denominator


-x*3x+18*3x+12*3x-2=0

Wy multiply elements

-3x^2+54x+36x-2=0

We add all the numbers together, and all the variables

-3x^2+90x-2=0

a = -3; b = 90; c = -2;
Δ = b2-4ac
Δ = 902-4·(-3)·(-2)
Δ = 8076
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:

$\sqrt{\Delta}=\sqrt{8076}=\sqrt{4*2019}=\sqrt{4}*\sqrt{2019}=2\sqrt{2019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2019}}{2*-3}=\frac{-90-2\sqrt{2019}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2019}}{2*-3}=\frac{-90+2\sqrt{2019}}{-6}
$