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40x^2+40x-1000=0
a = 40; b = 40; c = -1000;
Δ = b2-4ac
Δ = 402-4·40·(-1000)
Δ = 161600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{161600}=\sqrt{1600*101}=\sqrt{1600}*\sqrt{101}=40\sqrt{101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40\sqrt{101}}{2*40}=\frac{-40-40\sqrt{101}}{80} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40\sqrt{101}}{2*40}=\frac{-40+40\sqrt{101}}{80} $
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