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-5a^2-3a+22=0
a = -5; b = -3; c = +22;
Δ = b2-4ac
Δ = -32-4·(-5)·22
Δ = 449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{449}}{2*-5}=\frac{3-\sqrt{449}}{-10} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{449}}{2*-5}=\frac{3+\sqrt{449}}{-10} $
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