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12/x=5x+9
We move all terms to the left:
12/x-(5x+9)=0
Domain of the equation: x!=0We get rid of parentheses
x∈R
12/x-5x-9=0
We multiply all the terms by the denominator
-5x*x-9*x+12=0
We add all the numbers together, and all the variables
-9x-5x*x+12=0
Wy multiply elements
-5x^2-9x+12=0
a = -5; b = -9; c = +12;
Δ = b2-4ac
Δ = -92-4·(-5)·12
Δ = 321
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{-(-9)-\sqrt{321}}{2*-5}=\frac{9-\sqrt{321}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{321}}{2*-5}=\frac{9+\sqrt{321}}{-10} $
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