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X^2-3X-4014=0
a = 1; b = -3; c = -4014;
Δ = b2-4ac
Δ = -32-4·1·(-4014)
Δ = 16065
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16065}=\sqrt{9*1785}=\sqrt{9}*\sqrt{1785}=3\sqrt{1785}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{1785}}{2*1}=\frac{3-3\sqrt{1785}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{1785}}{2*1}=\frac{3+3\sqrt{1785}}{2} $
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