z2=47

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Solution for z2=47 equation:



z2=47
We move all terms to the left:
z2-(47)=0
We add all the numbers together, and all the variables
z^2-47=0
a = 1; b = 0; c = -47;
Δ = b2-4ac
Δ = 02-4·1·(-47)
Δ = 188
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:
$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{47}}{2*1}=\frac{0-2\sqrt{47}}{2} =-\frac{2\sqrt{47}}{2} =-\sqrt{47} $
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{47}}{2*1}=\frac{0+2\sqrt{47}}{2} =\frac{2\sqrt{47}}{2} =\sqrt{47} $

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