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1000-10x-4.9x^2=0
a = -4.9; b = -10; c = +1000;
Δ = b2-4ac
Δ = -102-4·(-4.9)·1000
Δ = 19700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19700}=\sqrt{100*197}=\sqrt{100}*\sqrt{197}=10\sqrt{197}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{197}}{2*-4.9}=\frac{10-10\sqrt{197}}{-9.8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{197}}{2*-4.9}=\frac{10+10\sqrt{197}}{-9.8} $
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