y2=38

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Solution for y2=38 equation:



y2=38
We move all terms to the left:
y2-(38)=0
We add all the numbers together, and all the variables
y^2-38=0
a = 1; b = 0; c = -38;
Δ = b2-4ac
Δ = 02-4·1·(-38)
Δ = 152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{38}}{2*1}=\frac{0-2\sqrt{38}}{2} =-\frac{2\sqrt{38}}{2} =-\sqrt{38} $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{38}}{2*1}=\frac{0+2\sqrt{38}}{2} =\frac{2\sqrt{38}}{2} =\sqrt{38} $

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