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5x+6/3x-9=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
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} $
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