18x-4-2/3x=16

Solution for 18x-4-2/3x=16 equation:

18x-4-2/3x=16

We move all terms to the left:

18x-4-2/3x-(16)=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-20=0

We multiply all the terms by the denominator


18x*3x-20*3x-2=0

Wy multiply elements

54x^2-60x-2=0

a = 54; b = -60; c = -2;
Δ = b2-4ac
Δ = -602-4·54·(-2)
Δ = 4032
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:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-24\sqrt{7}}{2*54}=\frac{60-24\sqrt{7}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+24\sqrt{7}}{2*54}=\frac{60+24\sqrt{7}}{108}
$