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 = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{41}}{2*15}=\frac{27-3\sqrt{41}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{41}}{2*15}=\frac{27+3\sqrt{41}}{30}
$