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3x-6/x+5=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
3x*x+5*x-6=0
We add all the numbers together, and all the variables
5x+3x*x-6=0
Wy multiply elements
3x^2+5x-6=0
a = 3; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·3·(-6)
Δ = 97
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{97}}{2*3}=\frac{-5-\sqrt{97}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{97}}{2*3}=\frac{-5+\sqrt{97}}{6} $
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