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10x^2+110x+242=0
a = 10; b = 110; c = +242;
Δ = b2-4ac
Δ = 1102-4·10·242
Δ = 2420
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2420}=\sqrt{484*5}=\sqrt{484}*\sqrt{5}=22\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-22\sqrt{5}}{2*10}=\frac{-110-22\sqrt{5}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+22\sqrt{5}}{2*10}=\frac{-110+22\sqrt{5}}{20} $
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