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x2-4x-4=12
We move all terms to the left:
x2-4x-4-(12)=0
We add all the numbers together, and all the variables
x^2-4x-16=0
a = 1; b = -4; c = -16;
Δ = b2-4ac
Δ = -42-4·1·(-16)
Δ = 80
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{5}}{2*1}=\frac{4-4\sqrt{5}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{5}}{2*1}=\frac{4+4\sqrt{5}}{2} $
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