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-0.1x^2+124x-3000=0
a = -0.1; b = 124; c = -3000;
Δ = b2-4ac
Δ = 1242-4·(-0.1)·(-3000)
Δ = 14176
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14176}=\sqrt{16*886}=\sqrt{16}*\sqrt{886}=4\sqrt{886}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-4\sqrt{886}}{2*-0.1}=\frac{-124-4\sqrt{886}}{-0.2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+4\sqrt{886}}{2*-0.1}=\frac{-124+4\sqrt{886}}{-0.2} $
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