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x^2-40x-125=0
a = 1; b = -40; c = -125;
Δ = b2-4ac
Δ = -402-4·1·(-125)
Δ = 2100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{21}}{2*1}=\frac{40-10\sqrt{21}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{21}}{2*1}=\frac{40+10\sqrt{21}}{2} $
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