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18x^2+33x-1=0
a = 18; b = 33; c = -1;
Δ = b2-4ac
Δ = 332-4·18·(-1)
Δ = 1161
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{129}}{2*18}=\frac{-33-3\sqrt{129}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{129}}{2*18}=\frac{-33+3\sqrt{129}}{36} $
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