4x-18/3x=0

Solution for 4x-18/3x=0 equation:

4x-18/3x=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


4x*3x-18=0

Wy multiply elements

12x^2-18=0

a = 12; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·12·(-18)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*12}=\frac{0-12\sqrt{6}}{24}
=-\frac{12\sqrt{6}}{24}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*12}=\frac{0+12\sqrt{6}}{24}
=\frac{12\sqrt{6}}{24}
=\frac{\sqrt{6}}{2}
$