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9x^2-1000x-200=0
a = 9; b = -1000; c = -200;
Δ = b2-4ac
Δ = -10002-4·9·(-200)
Δ = 1007200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1007200}=\sqrt{400*2518}=\sqrt{400}*\sqrt{2518}=20\sqrt{2518}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-20\sqrt{2518}}{2*9}=\frac{1000-20\sqrt{2518}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+20\sqrt{2518}}{2*9}=\frac{1000+20\sqrt{2518}}{18} $
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