5/3x-2x=18

Solution for 5/3x-2x=18 equation:

5/3x-2x=18

We move all terms to the left:

5/3x-2x-(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

-2x+5/3x-18=0

We multiply all the terms by the denominator


-2x*3x-18*3x+5=0

Wy multiply elements

-6x^2-54x+5=0

a = -6; b = -54; c = +5;
Δ = b2-4ac
Δ = -542-4·(-6)·5
Δ = 3036
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:

$\sqrt{\Delta}=\sqrt{3036}=\sqrt{4*759}=\sqrt{4}*\sqrt{759}=2\sqrt{759}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{759}}{2*-6}=\frac{54-2\sqrt{759}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{759}}{2*-6}=\frac{54+2\sqrt{759}}{-12}
$