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9x^2-21x-105=0
a = 9; b = -21; c = -105;
Δ = b2-4ac
Δ = -212-4·9·(-105)
Δ = 4221
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4221}=\sqrt{9*469}=\sqrt{9}*\sqrt{469}=3\sqrt{469}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{469}}{2*9}=\frac{21-3\sqrt{469}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{469}}{2*9}=\frac{21+3\sqrt{469}}{18} $
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