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12s^2-116s+19=0
a = 12; b = -116; c = +19;
Δ = b2-4ac
Δ = -1162-4·12·19
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{12544}=112$$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-112}{2*12}=\frac{4}{24} =1/6 $$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+112}{2*12}=\frac{228}{24} =9+1/2 $
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