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x^2-63x-972=0
a = 1; b = -63; c = -972;
Δ = b2-4ac
Δ = -632-4·1·(-972)
Δ = 7857
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7857}=\sqrt{81*97}=\sqrt{81}*\sqrt{97}=9\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-9\sqrt{97}}{2*1}=\frac{63-9\sqrt{97}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+9\sqrt{97}}{2*1}=\frac{63+9\sqrt{97}}{2} $
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