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9x^2-3x-840=0
a = 9; b = -3; c = -840;
Δ = b2-4ac
Δ = -32-4·9·(-840)
Δ = 30249
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{30249}=\sqrt{9*3361}=\sqrt{9}*\sqrt{3361}=3\sqrt{3361}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{3361}}{2*9}=\frac{3-3\sqrt{3361}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{3361}}{2*9}=\frac{3+3\sqrt{3361}}{18} $
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