x-5/3x-18=0

Solution for x-5/3x-18=0 equation:

x-5/3x-18=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

3x^2-54x-5=0

a = 3; b = -54; c = -5;
Δ = b2-4ac
Δ = -542-4·3·(-5)
Δ = 2976
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:

$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-4\sqrt{186}}{2*3}=\frac{54-4\sqrt{186}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+4\sqrt{186}}{2*3}=\frac{54+4\sqrt{186}}{6}
$