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102x-3150-0.1x^2=0
a = -0.1; b = 102; c = -3150;
Δ = b2-4ac
Δ = 1022-4·(-0.1)·(-3150)
Δ = 9144
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9144}=\sqrt{36*254}=\sqrt{36}*\sqrt{254}=6\sqrt{254}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-6\sqrt{254}}{2*-0.1}=\frac{-102-6\sqrt{254}}{-0.2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+6\sqrt{254}}{2*-0.1}=\frac{-102+6\sqrt{254}}{-0.2} $
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