4x(8-x)=8

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Solution for 4x(8-x)=8 equation:



4x(8-x)=8
We move all terms to the left:
4x(8-x)-(8)=0
We add all the numbers together, and all the variables
4x(-1x+8)-8=0
We multiply parentheses
-4x^2+32x-8=0
a = -4; b = 32; c = -8;
Δ = b2-4ac
Δ = 322-4·(-4)·(-8)
Δ = 896
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:
$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{14}}{2*-4}=\frac{-32-8\sqrt{14}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{14}}{2*-4}=\frac{-32+8\sqrt{14}}{-8} $

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