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6a^2+7-19a=0
a = 6; b = -19; c = +7;
Δ = b2-4ac
Δ = -192-4·6·7
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{193}}{2*6}=\frac{19-\sqrt{193}}{12} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{193}}{2*6}=\frac{19+\sqrt{193}}{12} $
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