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9x^2+39x-22=0
a = 9; b = 39; c = -22;
Δ = b2-4ac
Δ = 392-4·9·(-22)
Δ = 2313
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2313}=\sqrt{9*257}=\sqrt{9}*\sqrt{257}=3\sqrt{257}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{257}}{2*9}=\frac{-39-3\sqrt{257}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{257}}{2*9}=\frac{-39+3\sqrt{257}}{18} $
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