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19x^2-16x-19=0
a = 19; b = -16; c = -19;
Δ = b2-4ac
Δ = -162-4·19·(-19)
Δ = 1700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-10\sqrt{17}}{2*19}=\frac{16-10\sqrt{17}}{38} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+10\sqrt{17}}{2*19}=\frac{16+10\sqrt{17}}{38} $
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