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-9x^2-9x+3=0
a = -9; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·(-9)·3
Δ = 189
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{21}}{2*-9}=\frac{9-3\sqrt{21}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{21}}{2*-9}=\frac{9+3\sqrt{21}}{-18} $
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