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4x^2-33x-18=0
a = 4; b = -33; c = -18;
Δ = b2-4ac
Δ = -332-4·4·(-18)
Δ = 1377
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-9\sqrt{17}}{2*4}=\frac{33-9\sqrt{17}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+9\sqrt{17}}{2*4}=\frac{33+9\sqrt{17}}{8} $
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