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(8x-12=4x)(4x+8+20)
We move all terms to the left:
(8x-12-(4x)(4x+8+20))=0
We add all the numbers together, and all the variables
(8x-12-4x(4x+28))=0
We calculate terms in parentheses: +(8x-12-4x(4x+28)), so:We get rid of parentheses
8x-12-4x(4x+28)
determiningTheFunctionDomain 8x-4x(4x+28)-12
We multiply parentheses
-16x^2+8x-112x-12
We add all the numbers together, and all the variables
-16x^2-104x-12
Back to the equation:
+(-16x^2-104x-12)
-16x^2-104x-12=0
a = -16; b = -104; c = -12;
Δ = b2-4ac
Δ = -1042-4·(-16)·(-12)
Δ = 10048
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10048}=\sqrt{64*157}=\sqrt{64}*\sqrt{157}=8\sqrt{157}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-8\sqrt{157}}{2*-16}=\frac{104-8\sqrt{157}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+8\sqrt{157}}{2*-16}=\frac{104+8\sqrt{157}}{-32} $
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