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9-2x(3/x)=-1
We move all terms to the left:
9-2x(3/x)-(-1)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
-2x(+3/x)+9-(-1)=0
We add all the numbers together, and all the variables
-2x(+3/x)+10=0
We multiply parentheses
-6x^2+10=0
a = -6; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-6)·10
Δ = 240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-6}=\frac{0-4\sqrt{15}}{-12} =-\frac{4\sqrt{15}}{-12} =-\frac{\sqrt{15}}{-3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-6}=\frac{0+4\sqrt{15}}{-12} =\frac{4\sqrt{15}}{-12} =\frac{\sqrt{15}}{-3} $
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