0=80(8+x)(8-x)

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Solution for 0=80(8+x)(8-x) equation:



0=80(8+x)(8-x)
We move all terms to the left:
0-(80(8+x)(8-x))=0
We add all the numbers together, and all the variables
-(80(x+8)(-1x+8))+0=0
We add all the numbers together, and all the variables
-(80(x+8)(-1x+8))=0
We multiply parentheses ..
-(80(-1x^2+8x-8x+64))=0
We calculate terms in parentheses: -(80(-1x^2+8x-8x+64)), so:
80(-1x^2+8x-8x+64)
We multiply parentheses
-80x^2+640x-640x+5120
We add all the numbers together, and all the variables
-80x^2+5120
Back to the equation:
-(-80x^2+5120)
We get rid of parentheses
80x^2-5120=0
a = 80; b = 0; c = -5120;
Δ = b2-4ac
Δ = 02-4·80·(-5120)
Δ = 1638400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1638400}=1280$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1280}{2*80}=\frac{-1280}{160} =-8 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1280}{2*80}=\frac{1280}{160} =8 $

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