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x^2-120x+1440=0
a = 1; b = -120; c = +1440;
Δ = b2-4ac
Δ = -1202-4·1·1440
Δ = 8640
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8640}=\sqrt{576*15}=\sqrt{576}*\sqrt{15}=24\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-24\sqrt{15}}{2*1}=\frac{120-24\sqrt{15}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+24\sqrt{15}}{2*1}=\frac{120+24\sqrt{15}}{2} $
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