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0=y2+8y+9
We move all terms to the left:
0-(y2+8y+9)=0
We add all the numbers together, and all the variables
-(+y^2+8y+9)+0=0
We add all the numbers together, and all the variables
-(+y^2+8y+9)=0
We get rid of parentheses
-y^2-8y-9=0
We add all the numbers together, and all the variables
-1y^2-8y-9=0
a = -1; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·(-1)·(-9)
Δ = 28
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{7}}{2*-1}=\frac{8-2\sqrt{7}}{-2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{7}}{2*-1}=\frac{8+2\sqrt{7}}{-2} $
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