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=(6Y+8)(4.5Y+12)-(2Y+4)(2.5Y+8)
We move all terms to the left:
-((6Y+8)(4.5Y+12)-(2Y+4)(2.5Y+8))=0
We multiply parentheses ..
-((+24Y^2+72Y+32Y+96)-(2Y+4)(2.5Y+8))=0
We calculate terms in parentheses: -((+24Y^2+72Y+32Y+96)-(2Y+4)(2.5Y+8)), so:We get rid of parentheses
(+24Y^2+72Y+32Y+96)-(2Y+4)(2.5Y+8)
We get rid of parentheses
24Y^2+72Y+32Y-(2Y+4)(2.5Y+8)+96
We multiply parentheses ..
24Y^2-(+4Y^2+16Y+8Y+32)+72Y+32Y+96
We add all the numbers together, and all the variables
24Y^2-(+4Y^2+16Y+8Y+32)+104Y+96
We get rid of parentheses
24Y^2-4Y^2-16Y-8Y+104Y-32+96
We add all the numbers together, and all the variables
20Y^2+80Y+64
Back to the equation:
-(20Y^2+80Y+64)
-20Y^2-80Y-64=0
a = -20; b = -80; c = -64;
Δ = b2-4ac
Δ = -802-4·(-20)·(-64)
Δ = 1280
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}$$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16\sqrt{5}}{2*-20}=\frac{80-16\sqrt{5}}{-40} $$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16\sqrt{5}}{2*-20}=\frac{80+16\sqrt{5}}{-40} $
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