2/3x-18x=27

Solution for 2/3x-18x=27 equation:

2/3x-18x=27

We move all terms to the left:

2/3x-18x-(27)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-18x+2/3x-27=0

We multiply all the terms by the denominator


-18x*3x-27*3x+2=0

Wy multiply elements

-54x^2-81x+2=0

a = -54; b = -81; c = +2;
Δ = b2-4ac
Δ = -812-4·(-54)·2
Δ = 6993
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:

$\sqrt{\Delta}=\sqrt{6993}=\sqrt{9*777}=\sqrt{9}*\sqrt{777}=3\sqrt{777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{777}}{2*-54}=\frac{81-3\sqrt{777}}{-108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{777}}{2*-54}=\frac{81+3\sqrt{777}}{-108}
$