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x(x-4)=44
We move all terms to the left:
x(x-4)-(44)=0
We multiply parentheses
x^2-4x-44=0
a = 1; b = -4; c = -44;
Δ = b2-4ac
Δ = -42-4·1·(-44)
Δ = 192
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{3}}{2*1}=\frac{4-8\sqrt{3}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{3}}{2*1}=\frac{4+8\sqrt{3}}{2} $
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