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u^2+22u+5=0
a = 1; b = 22; c = +5;
Δ = b2-4ac
Δ = 222-4·1·5
Δ = 464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-4\sqrt{29}}{2*1}=\frac{-22-4\sqrt{29}}{2} $$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+4\sqrt{29}}{2*1}=\frac{-22+4\sqrt{29}}{2} $
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