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=(2Y-2)(4Y-8)
We move all terms to the left:
-((2Y-2)(4Y-8))=0
We multiply parentheses ..
-((+8Y^2-16Y-8Y+16))=0
We calculate terms in parentheses: -((+8Y^2-16Y-8Y+16)), so:We get rid of parentheses
(+8Y^2-16Y-8Y+16)
We get rid of parentheses
8Y^2-16Y-8Y+16
We add all the numbers together, and all the variables
8Y^2-24Y+16
Back to the equation:
-(8Y^2-24Y+16)
-8Y^2+24Y-16=0
a = -8; b = 24; c = -16;
Δ = b2-4ac
Δ = 242-4·(-8)·(-16)
Δ = 64
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{64}=8$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8}{2*-8}=\frac{-32}{-16} =+2 $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8}{2*-8}=\frac{-16}{-16} =1 $
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