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(2+y)(8-y)=8
We move all terms to the left:
(2+y)(8-y)-(8)=0
We add all the numbers together, and all the variables
(y+2)(-1y+8)-8=0
We multiply parentheses ..
(-1y^2+8y-2y+16)-8=0
We get rid of parentheses
-1y^2+8y-2y+16-8=0
We add all the numbers together, and all the variables
-1y^2+6y+8=0
a = -1; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·(-1)·8
Δ = 68
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*-1}=\frac{-6-2\sqrt{17}}{-2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*-1}=\frac{-6+2\sqrt{17}}{-2} $
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