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22-17x-3x^2=0
a = -3; b = -17; c = +22;
Δ = b2-4ac
Δ = -172-4·(-3)·22
Δ = 553
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{553}}{2*-3}=\frac{17-\sqrt{553}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{553}}{2*-3}=\frac{17+\sqrt{553}}{-6} $
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