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-0.2x^2+100x-3000=0
a = -0.2; b = 100; c = -3000;
Δ = b2-4ac
Δ = 1002-4·(-0.2)·(-3000)
Δ = 7600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7600}=\sqrt{400*19}=\sqrt{400}*\sqrt{19}=20\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{19}}{2*-0.2}=\frac{-100-20\sqrt{19}}{-0.4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{19}}{2*-0.2}=\frac{-100+20\sqrt{19}}{-0.4} $
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