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8+4x(x-32)=64
We move all terms to the left:
8+4x(x-32)-(64)=0
We add all the numbers together, and all the variables
4x(x-32)-56=0
We multiply parentheses
4x^2-128x-56=0
a = 4; b = -128; c = -56;
Δ = b2-4ac
Δ = -1282-4·4·(-56)
Δ = 17280
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17280}=\sqrt{576*30}=\sqrt{576}*\sqrt{30}=24\sqrt{30}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-24\sqrt{30}}{2*4}=\frac{128-24\sqrt{30}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+24\sqrt{30}}{2*4}=\frac{128+24\sqrt{30}}{8} $
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