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9(9z*9)(9z*9)=399.500
We move all terms to the left:
9(9z*9)(9z*9)-(399.500)=0
We add all the numbers together, and all the variables
9(+9z*9)(+9z*9)-(399.5)=0
We add all the numbers together, and all the variables
9(+9z*9)(+9z*9)-399.5=0
We multiply parentheses ..
9(+6561z^2)-399.5=0
We multiply parentheses
59049z^2-399.5=0
a = 59049; b = 0; c = -399.5;
Δ = b2-4ac
Δ = 02-4·59049·(-399.5)
Δ = 94360302
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}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{94360302}=\sqrt{59049*1598}=\sqrt{59049}*\sqrt{1598}=243\sqrt{1598}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-243\sqrt{1598}}{2*59049}=\frac{0-243\sqrt{1598}}{118098} =-\frac{243\sqrt{1598}}{118098} =-\frac{\sqrt{1598}}{486} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+243\sqrt{1598}}{2*59049}=\frac{0+243\sqrt{1598}}{118098} =\frac{243\sqrt{1598}}{118098} =\frac{\sqrt{1598}}{486} $
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