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X^2-4X-183=0

a = 1; b = -4; c = -183;

Δ = b^{2}-4ac

Δ = -4^{2}-4·1·(-183)

Δ = 748

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{748}=\sqrt{4*187}=\sqrt{4}*\sqrt{187}=2\sqrt{187}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{187}}{2*1}=\frac{4-2\sqrt{187}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{187}}{2*1}=\frac{4+2\sqrt{187}}{2} $

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