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165000x^2-9500x-292032=0
a = 165000; b = -9500; c = -292032;
Δ = b2-4ac
Δ = -95002-4·165000·(-292032)
Δ = 192831370000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{192831370000}=\sqrt{10000*19283137}=\sqrt{10000}*\sqrt{19283137}=100\sqrt{19283137}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9500)-100\sqrt{19283137}}{2*165000}=\frac{9500-100\sqrt{19283137}}{330000} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9500)+100\sqrt{19283137}}{2*165000}=\frac{9500+100\sqrt{19283137}}{330000} $
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