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-16x^2-400x-1000=0
a = -16; b = -400; c = -1000;
Δ = b2-4ac
Δ = -4002-4·(-16)·(-1000)
Δ = 96000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{96000}=\sqrt{6400*15}=\sqrt{6400}*\sqrt{15}=80\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-80\sqrt{15}}{2*-16}=\frac{400-80\sqrt{15}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+80\sqrt{15}}{2*-16}=\frac{400+80\sqrt{15}}{-32} $
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