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X^2-3X-1296=0
a = 1; b = -3; c = -1296;
Δ = b2-4ac
Δ = -32-4·1·(-1296)
Δ = 5193
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5193}=\sqrt{9*577}=\sqrt{9}*\sqrt{577}=3\sqrt{577}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{577}}{2*1}=\frac{3-3\sqrt{577}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{577}}{2*1}=\frac{3+3\sqrt{577}}{2} $
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