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y(2)=y+47
We move all terms to the left:
y(2)-(y+47)=0
We add all the numbers together, and all the variables
y^2-(y+47)=0
We get rid of parentheses
y^2-y-47=0
We add all the numbers together, and all the variables
y^2-1y-47=0
a = 1; b = -1; c = -47;
Δ = b2-4ac
Δ = -12-4·1·(-47)
Δ = 189
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{21}}{2*1}=\frac{1-3\sqrt{21}}{2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{21}}{2*1}=\frac{1+3\sqrt{21}}{2} $
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