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3x^2-21x-117=0
a = 3; b = -21; c = -117;
Δ = b2-4ac
Δ = -212-4·3·(-117)
Δ = 1845
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1845}=\sqrt{9*205}=\sqrt{9}*\sqrt{205}=3\sqrt{205}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{205}}{2*3}=\frac{21-3\sqrt{205}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{205}}{2*3}=\frac{21+3\sqrt{205}}{6} $
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