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10x^2-100x+122=0
a = 10; b = -100; c = +122;
Δ = b2-4ac
Δ = -1002-4·10·122
Δ = 5120
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5120}=\sqrt{1024*5}=\sqrt{1024}*\sqrt{5}=32\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-32\sqrt{5}}{2*10}=\frac{100-32\sqrt{5}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+32\sqrt{5}}{2*10}=\frac{100+32\sqrt{5}}{20} $
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