Solve $5x^2-6x-2=0$ using the quadratic formula.

$D=36-4(5)(-2)=36+40=76$, so $x=\frac{6\pm \sqrt{76}}{10}=\frac{6\pm 2\sqrt{19}}{10}=\frac{3\pm \sqrt{19}}{5}$. The first option flips the sign of −b. The third option is correct before simplifying but was then "simplified" by halving only the 6 and the 10 while leaving $\sqrt{76}$ untouched. The last option halves the numerator and denominator without taking the factor 2 out of $\sqrt{76}$ first.