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81x^2-18x-100=0
a = 81; b = -18; c = -100;
Δ = b2-4ac
Δ = -182-4·81·(-100)
Δ = 32724
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32724}=\sqrt{324*101}=\sqrt{324}*\sqrt{101}=18\sqrt{101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{101}}{2*81}=\frac{18-18\sqrt{101}}{162} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{101}}{2*81}=\frac{18+18\sqrt{101}}{162} $
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