5x-6/3x-9=0

Solution for 5x-6/3x-9=0 equation:

5x-6/3x-9=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


5x*3x-9*3x-6=0

Wy multiply elements

15x^2-27x-6=0

a = 15; b = -27; c = -6;
Δ = b2-4ac
Δ = -272-4·15·(-6)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-33}{2*15}=\frac{-6}{30}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+33}{2*15}=\frac{60}{30}
=2
$