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50x^2-20x-181=0
a = 50; b = -20; c = -181;
Δ = b2-4ac
Δ = -202-4·50·(-181)
Δ = 36600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36600}=\sqrt{100*366}=\sqrt{100}*\sqrt{366}=10\sqrt{366}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{366}}{2*50}=\frac{20-10\sqrt{366}}{100} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{366}}{2*50}=\frac{20+10\sqrt{366}}{100} $
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