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19.686x^2-131.436x+124.14=0
a = 19.686; b = -131.436; c = +124.14;
Δ = b2-4ac
Δ = -131.4362-4·19.686·124.14
Δ = 7500.141936
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{-(-131.436)-\sqrt{7500.141936}}{2*19.686}=\frac{131.436-\sqrt{7500.141936}}{39.372} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-131.436)+\sqrt{7500.141936}}{2*19.686}=\frac{131.436+\sqrt{7500.141936}}{39.372} $
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