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18x^2+33x-2=0
a = 18; b = 33; c = -2;
Δ = b2-4ac
Δ = 332-4·18·(-2)
Δ = 1233
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{137}}{2*18}=\frac{-33-3\sqrt{137}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{137}}{2*18}=\frac{-33+3\sqrt{137}}{36} $
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