-3/z=-9z

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Solution for -3/z=-9z equation:



-3/z=-9z
We move all terms to the left:
-3/z-(-9z)=0
Domain of the equation: z!=0
z∈R
We get rid of parentheses
-3/z+9z=0
We multiply all the terms by the denominator
9z*z-3=0
Wy multiply elements
9z^2-3=0
a = 9; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·9·(-3)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3}}{2*9}=\frac{0-6\sqrt{3}}{18} =-\frac{6\sqrt{3}}{18} =-\frac{\sqrt{3}}{3} $
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3}}{2*9}=\frac{0+6\sqrt{3}}{18} =\frac{6\sqrt{3}}{18} =\frac{\sqrt{3}}{3} $

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